# Math question help

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I get how to do this question

Attachment 720496720498

But was just wondering.. Isn’t a

Attachment 720496720498

But was just wondering.. Isn’t a

_{k}= (-2)^(k-1) the kth term of a geometric sequence because we’re multiplying by -2 each time?
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(Original post by

Yes you are right

**Hammad(214508)**)Yes you are right

Also, I get how to do this question as well.

Attachment 720500720504

But was just wondering.. Isn’t a

_{k}=2^k the kth term of a geometric sequence because we’re multiplying by 2 each time?

For a

_{k}=2^k to be the kth term of a geometric sequence also doesn’t make sense though, and I have explained this below:

a

_{0}=1

a

_{1 }=2

a

_{2 }=4

a

_{3 }=8

a

_{4 }=16

We are multiplying by 2 each time. The first term (a

_{1 }=2 not a

_{0 }=1) is 2.

Using the formula a

_{k }=ar

^{k-1}, the kth term of the geometric sequence is a

_{k }=2 x 2

^{k-1}. This doesn’t make sense as the kth term mentioned in the question for this sequence is a

_{k}=2^k..

Could you please help me understand this?

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#4

(Original post by

Thanks very much!

Also, I get how to do this question as well.

Attachment 720500720504

But was just wondering.. Isn’t a

For a

a

a

a

We are multiplying by 2 each time. The first term (a

Using the formula a

Could you please help me understand this?

**sienna2266**)Thanks very much!

Also, I get how to do this question as well.

Attachment 720500720504

But was just wondering.. Isn’t a

_{k}=2^k the kth term of a geometric sequence because we’re multiplying by 2 each time?For a

_{k}=2^k to be the kth term of a geometric sequence also doesn’t make sense though, and I have explained this below:a

_{0}=1a_{1 }=2a_{2 }=4a

_{3 }=8a

_{4 }=16We are multiplying by 2 each time. The first term (a

_{1 }=2 not a_{0 }=1) is 2.Using the formula a

_{k }=ar^{k-1}, the kth term of the geometric sequence is a_{k }=2 x 2^{k-1}. This doesn’t make sense as the kth term mentioned in the question for this sequence is a_{k}=2^k..Could you please help me understand this?

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(Original post by

Look at the number below the sigma notation, the first one start with 1, while the second one starts at 1 (1 to 4)

**Hammad(214508)**)Look at the number below the sigma notation, the first one start with 1, while the second one starts at 1 (1 to 4)

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#6

(Original post by

Using the formula a

Could you please help me understand this?

**sienna2266**)Using the formula a

_{k }=ar^{k-1}, the kth term of the geometric sequence is a_{k }=2 x 2^{k-1}. This doesn’t make sense as the kth term mentioned in the question for this sequence is a_{k}=2^k..Could you please help me understand this?

Of a geo sequence, does not specify the kth term, it specifies the (k+1)th term. But does specify the kth term, and note that

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(Original post by

Don't understand your question TBH.

Of a geo sequence, does not specify the kth term, it specifies the (k+1)th term. But does specify the kth term, and note that

**RDKGames**)Don't understand your question TBH.

Of a geo sequence, does not specify the kth term, it specifies the (k+1)th term. But does specify the kth term, and note that

Just to double check:

2iii) is a geometric series, right?

And the first term of this geometric series is a1=2 and not a0=1 right?

1(iv) is a geometric series as well?

And the first term of this geometric series is a1=1?

So a1 is pretty much the first term for any geometric/arithmetic series/sequence?

Many thanks

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#8

(Original post by

Ahh this makes sense cause 2 x2^(k-1) is the same thing as 2^k!

Just to double check:

2iii) is a geometric series, right?

And the first term of this geometric series is a1=2 and not a0=1 right?

**sienna2266**)Ahh this makes sense cause 2 x2^(k-1) is the same thing as 2^k!

Just to double check:

2iii) is a geometric series, right?

And the first term of this geometric series is a1=2 and not a0=1 right?

(Original post by

1(iv) is a geometric series as well?

And the first term of this geometric series is a1=1?

**sienna2266**)1(iv) is a geometric series as well?

And the first term of this geometric series is a1=1?

(Original post by

So a1 is pretty much the first term for any geometric/arithmetic series/sequence?

**sienna2266**)So a1 is pretty much the first term for any geometric/arithmetic series/sequence?

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(Original post by

It's a geometric series of the sequence with .

It's a geometric series of a sequence with

Yes, you want to correspond to the 1st term of your sequence. Wouldn't make much sense to refer to the '0th' term

**RDKGames**)It's a geometric series of the sequence with .

It's a geometric series of a sequence with

Yes, you want to correspond to the 1st term of your sequence. Wouldn't make much sense to refer to the '0th' term

I have just attached it here again:

Attachment 720514720516

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#10

(Original post by

Thanks, but isn't 2iii) ak = 2^k or ak=2 x 2^(k-1)? Also, shouldn't a1 = 2?

I have just attached it here again:

**sienna2266**)Thanks, but isn't 2iii) ak = 2^k or ak=2 x 2^(k-1)? Also, shouldn't a1 = 2?

I have just attached it here again:

Note that then map and we have which is the sum of the sequence from the first term up to the 5th term.

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(Original post by

If it starts at 2, then you're completely ignoring the actual first term of 1.

Note that then map and we have which is the sum of the sequence from the first term up to the 5th term.

**RDKGames**)If it starts at 2, then you're completely ignoring the actual first term of 1.

Note that then map and we have which is the sum of the sequence from the first term up to the 5th term.

If you are given

a

_{0}=1

a

_{1 }=2

a

_{2 }=4

a

_{3 }=8

a

_{4 }=16

and asked to write out the sequence formula for this...

The first term is a0 which is 1 (this doesn't sound right because a1 should be the first term but then 1 is the first term in the sequence so I am confused here).

The kth term of the sequence using the formula ak = ar^(k-1) and the fact that first term=a0=1, is ak=1 x 2^(k-1) --> ak= 2^(k-1).

However, in the question, ak= 2^k from the sequence a0 to a4.

Instead, if we take the first term as a1 which is 2 (this also doesn't sound right because 2 is the second term in the sequence).

The kth of the sequence using the formula ak= ar^(k-1) and the fact that first term=a1=2,

is ak= 2 x 2^(k-1) which is the same thing as ak= 2^k. And in the question, ak= 2^k.

Could you please help me with this? Many thanks

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#12

(Original post by

...

**sienna2266**)...

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This is shown here:

r=2 and a0=1

Sub them both into the formula ak=ar^(k-1) and you get ak=2^(k-1) and not ak=2^k.

In the picture I have attached here, ak=2^k where a0=1,a1=2,a2=4,a3=8 and a4=16

so why is it only when we sub a1=2 into ak=ar^(k-1), that we get ak=2^k?

As you said, "the formula is just if you start from as the initial term" but this is not the case here.

Would really appreciate if you could please let me know what you think. Many thanks.

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#14

(Original post by

But the thing is if you start from a0 as the initial term, the kth term of the sequence is ak=2^(k-1).

This is shown here:

r=2 and a0=1

Sub them both into the formula ak=ar^(k-1) and you get ak=2^(k-1) and not ak=2^k.

In the picture I have attached here, ak=2^k where a0=1,a1=2,a2=4,a3=8 and a4=16

so why is it only when we sub a1=2 into ak=ar^(k-1), that we get ak=2^k?

As you said, "the formula is just if you start from as the initial term" but this is not the case here.

Would really appreciate if you could please let me know what you think. Many thanks.

**sienna2266**)But the thing is if you start from a0 as the initial term, the kth term of the sequence is ak=2^(k-1).

This is shown here:

r=2 and a0=1

Sub them both into the formula ak=ar^(k-1) and you get ak=2^(k-1) and not ak=2^k.

In the picture I have attached here, ak=2^k where a0=1,a1=2,a2=4,a3=8 and a4=16

so why is it only when we sub a1=2 into ak=ar^(k-1), that we get ak=2^k?

As you said, "the formula is just if you start from as the initial term" but this is not the case here.

Would really appreciate if you could please let me know what you think. Many thanks.

Look, is just a different way to write the sum of the first 5 terms of the sequence for . This sequence does not carry the notion of having a 0th term because this sequence starts with .

If you decide to allow the 0th term as a thing, then the sequence is for so that and we can say that the kth term here is but we have to start with 0th term. So when you say 2nd term, you're really referring to the 3rd one down the line.

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(Original post by

If you decide to allow the 0th term as a thing, then the sequence is for so that and we can say that the kth term here is but we have to start with 0th term. So when you say 2nd term, you're really referring to the 3rd one down the line.

**RDKGames**)If you decide to allow the 0th term as a thing, then the sequence is for so that and we can say that the kth term here is but we have to start with 0th term. So when you say 2nd term, you're really referring to the 3rd one down the line.

So to get ak=2^k from the sequence 1,2,4,4,16 you sub in r=2 and and a1=2 (cause the first term is 2 and 0th term is 1) into ak=ar^(k-1).

Please kindly let me know about my progress😅

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