Year 12s: what will be the first way you research your future options? >>

Year 12s: what will be the first way you research your future options? >>

Year 12s: what will be the first way you research your future options? >>

Sequences and Series C2

Help me this question.
geometric progression
a3 = 16, a4 = 12.8, find a and r

Study Forum Helper

\displaystyle r=\frac{a_4}{a_3}

OP

i get it thanks xD

S_n = 2^(2n-1)-2 find a and r

OP

Original post by NKenny

i get it thanks xD

S_n = 2^(2n-1)-2 find a and r

from this question I don't understand this bit.

a_k is k term
and S_n is sum of n term

both is the term but why is it have 2 different letter

Study Forum Helper

Original post by NKenny

from this question I don't understand this bit.

a_k is k term
and S_n is sum of n term

both is the term but why is it have 2 different letter

k refers to a particular term. There are a total of n terms.

OP

Original post by Mr M

k refers to a particular term. There are a total of n terms.

so S₄ = a₁+... +a₄ rite ?

and what about geometric progression and geometric series. are they the same thing ?

SebastianTindall

Could anyone give me a hand with some sigma notation?

I am supposed to find the sum of 8 terms starting from term 3 with the general formula of (k^2-1), is this Geometric or Arithmetic? can i use the formula's or do i have to work out each term and add them?

Original post by SebastianTindall

Could anyone give me a hand with some sigma notation?

I am supposed to find the sum of 8 terms starting from term 3 with the general formula of (k^2-1), is this Geometric or Arithmetic? can i use the formula's or do i have to work out each term and add them?

Is this what you wanted?

Spoiler

There is a formula for the sum of k² it's covered in FP1, what level of maths do you do?

Original post by SebastianTindall

Could anyone give me a hand with some sigma notation?

I am supposed to find the sum of 8 terms starting from term 3 with the general formula of (k^2-1), is this Geometric or Arithmetic? can i use the formula's or do i have to work out each term and add them?

Your first term is 3 so k=2 (2^2-1=3)
For the last term k=9
THe question is

\displaystyle \sum_{k=2}^9 (k^2-1)=\sum_{k=2}^9 k^2 -\sum_{k=2}^9 1=

\displaystyle \sum_{k=1}^9 k^2 -1^2-8=\sum_{k=1}^9 k^2 -9

And as it known

\sum_{k=1}^n k^2=\frac{n\cdot (n+1)\cdot (2n+1)}{6}

Study Forum Helper

Original post by NKenny

and what about geometric progression and geometric series. are they the same thing ?

Here is an example of a geometric progression:

1, 2, 4, 8, 16, 32

Here is an example of a geometric series:

1 + 2 + 4 + 8 + 16 + 32

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