I am given the geometric sequence 2,8,32,128..

I am asked to find the smallest n for Sn>5000

I know a=2 , r=4

Using Sn=a(1-r^n)/1-r

We get,

5000< 2(1-4^n)/1-4

I find that n=6.44 to 2. d.p. Nothing states in the question that it must be a whole number..

Is my working out correct?

I am asked to find the smallest n for Sn>5000

I know a=2 , r=4

Using Sn=a(1-r^n)/1-r

We get,

5000< 2(1-4^n)/1-4

I find that n=6.44 to 2. d.p. Nothing states in the question that it must be a whole number..

Is my working out correct?

(edited 3 months ago)

Original post by KingRich

I am given the geometric sequence 2,8,32,128..

I am asked to find the smallest n for Sn>5000

I know a=2 , r=4

Using Sn=a(1-r^n)/1-r

We get,

5000< 2(1-4^n)/1-4

I find that n=6.44 to 2. d.p. Nothing states in the question that it must be a whole number..

Is my working out correct?

I am asked to find the smallest n for Sn>5000

I know a=2 , r=4

Using Sn=a(1-r^n)/1-r

We get,

5000< 2(1-4^n)/1-4

I find that n=6.44 to 2. d.p. Nothing states in the question that it must be a whole number..

Is my working out correct?

Its pretty much implied that its an integer so round up to get the smallest integer satisfying the inequality. The original sequence is defined in terms of n=1,2,3,... and having a term with an index of 2.44 wouldnt make sense.

Note the question is a bit imprecise about whether the first term corresponds to n=0 or n=1 and that obviously affects the answer.

Also in this case its easier to write the sum as

a(r^n-1)/(r-1)

as it keeps things positive. You seem to lose the inequality flips during your working.

(edited 3 months ago)

Original post by mqb2766

Its pretty much implied that its an integer so round up to get the smallest integer satisfying the inequality.

Note the question is a bit imprecise about whether the first term corresponds to n=0 or n=1 and that obviously affects the answer.

Also in this case its easier to write the sum as

a(r^n-1)/(r-1)

as it keeps things positive. You seem to lose the inequality flips during your working.

Note the question is a bit imprecise about whether the first term corresponds to n=0 or n=1 and that obviously affects the answer.

Also in this case its easier to write the sum as

a(r^n-1)/(r-1)

as it keeps things positive. You seem to lose the inequality flips during your working.

Crap, of course when I multiply -1 the sign is meant to change direction. I’ll boil it down to me misunderstanding the question then 🙂

Original post by KingRich

Crap, of course when I multiply -1 the sign is meant to change direction. I’ll boil it down to me misunderstanding the question then 🙂

Note what youve posted the question could be either find n (text) or find Sn (image).

Original post by mqb2766

Note what youve posted the question could be either find n (text) or find Sn (image).

What do you mean? Sn(image) as in the Sn=Σ thing?…

I can't recall the actual words but it was something like find the smallest n value for where Sn<5000...

Original post by KingRich

What do you mean? Sn(image) as in the Sn=Σ thing?…

I can't recall the actual words but it was something like find the smallest n value for where Sn<5000...

I can't recall the actual words but it was something like find the smallest n value for where Sn<5000...

You could either ask for the value of the index (n or n-1) or the value of the sum. Either/both is fine, but writing "smallest Sn > 500" is different from "smallest n such that Sn > 5000". Not a big deal.

Original post by mqb2766

You could either ask for the value of the index (n or n-1) or the value of the sum. Either/both is fine, but writing "smallest Sn > 500" is different from "smallest n such that Sn > 5000". Not a big deal.

Mmm, I’ll find the question tomorrow and send it tomorrow. Perhaps, it’s another bad structured question. Lol

Original post by mqb2766

You could either ask for the value of the index (n or n-1) or the value of the sum. Either/both is fine, but writing "smallest Sn > 500" is different from "smallest n such that Sn > 5000". Not a big deal.

This is the equation

Original post by KingRich

This is the equation

So youve got the answer?

Note that a duffers solution would simply be to list the values (as r is fairly large so n will be small)

2,8,32,128,512,2048,...

and even without summing them it would be fairly clear that the next one would tip you over the 5000 value

Original post by mqb2766

So youve got the answer?

Note that a duffers solution would simply be to list the values (as r is fairly large so n will be small)

2,8,32,128,512,2048,...

and even without summing them it would be fairly clear that the next one would tip you over the 5000 value

Note that a duffers solution would simply be to list the values (as r is fairly large so n will be small)

2,8,32,128,512,2048,...

and even without summing them it would be fairly clear that the next one would tip you over the 5000 value

Well, I know r=4, so the solution was is n=7, however, I applied the log to find the closest to be 6.44 without considering that they were asking for a whole number.

Original post by KingRich

Well, I know r=4, so the solution was is n=7, however, I applied the log to find the closest to be 6.44 without considering that they were asking for a whole number.

That wouild be the expected solution to the question, though youd note that n must be a positive integer (original sequence index) so the answer would be 7.

Original post by mqb2766

That wouild be the expected solution to the question, though youd note that n must be a positive integer (original sequence index) so the answer would be 7.

Yeah, I think I was just more confident the fact that I could recall the log approach, so either way, I'm happy. I mean I don't get marked on that question, so it's not an issue

- Question about Un = Sn - S(n-1) formula (Sequences and series)
- Electrochemistry help
- Math Proof Questions
- Arithmetic sequence diverge or converge formula?
- Dating need assistance
- What car has everything you want ultimate dream car
- Grad Scheme Advice (which to pick?!)
- Grant Thornton final interview
- Grant thornton 2024 entry
- OCRA A level chemistry 2024 paper 2
- Should I work for a Big 4 firm?
- Bank of America apprenticeship 2023
- 2024 Grant Thornton apprenticeship application thread
- Grant Thornton School Leaver 2023 entry x
- Pre-registration paramedic science degree at University of West London
- Not received assessment invitation from Grant Thornton yet...
- Edexcel IGCSE Higher tier Mathematics A Paper 1 1H (4MA1) - 16th May 2024 [Exam Chat]
- grant thornton digital interview
- New Spec A Level Sequences
- Grant Thornton final interview

Latest

Trending