Question

1. Which of the following is the sum of the first 15 terms of the series 2, -12, 72, ...?
2.
What is sum of the first 20 terms of the series -3, 0, 3, ...?
3. What is the sum of the first 30 terms of the series 9, 3, 1, ...?

Answer 1

well the series seems to be geometric... can you identify the common ratio...?

Answer 2

question 2. seems to be arithmetic.... can you identify the common difference

Question 3. seems to be geometric... so you need a common ratio.

Answer 3

Im just extremely confused... can you explain this to me at all?

Answer 4

on.... question 1 is a geometric series...

you are multiplying the 1st term by a value to get the 2nd term...

and then the 2nd term is multiplied by the same vale to get the 3rd term... etc...

so the multiplying value is called the common ratio

so

2 x ? = -12

-12 x ? = 72

any ideas of ?

Answer 5

Yes, you have to multiply each term by -6

Answer 6

great you have the common ratio... so you need the formula for the sum of a geometric series

\[S_{n} = \frac{a_{1}\times ( 1 - r^n)}{1 - r}\]

in question 1. n = 15, a1 is the 1st term = 2 and r = -6

so substituting

\[S_{15} = \frac{2 \times(1 - (-6)^{15})}{1 - (-6)}\]

so now you can calculate the sum

Answer 7

Would it be 134338567022?

Answer 8

-2.5 x 1010

2.5 x 1010

-1.3 x 1011

1.3 x 1011
these are my options so Im confused

Answer 9

yep... that looks correct...

now question 2... its an arithmetic sequence

and the sum is

\[S_{n} = \frac{n}{2} [ 2a_{1} + (n - 1) \times d]\]

you know n = 20, a1 = -3..... you need to find d, which is what is added to each term..

substitute into the formula as calculate

Answer 10

Wait can you look at my previous response to help me determine which is the answer for number 1? I got 510 for number 2

Answer 11

its the last one

Answer 12

thats correct... for 2

now look at 3... its geometric... so what do you multiply by...?

Answer 13

3

Answer 14

no, you're dividing by 3... so how do you write that as a multiplication...?

Answer 15

14.14?

Answer 16

Now how would i solve this? Find the 40th term of the sequence 2, -12, 72

Answer 17

well this is the 1st question again, with n = 40

Answer 18

But its not the sum, just finding the 40th term

Answer 19

for the 3rd question, the common ratio r = 1/3

a1 = 9 and n = 30

go back and use the geometric sum formula that's posted for the 1st question

Answer 20

Wouldn't it come out to 14.14?

Answer 21

well I got 13.5

Answer 22

Oh I see my mistake now in one of my calculations, Thanks! Could you just help me with th last one finding the 40th term?

Answer 23

well the 40th term question uses the same sequence as the 1st sequence just looking at things... all that is changed is n = 40

so redo question 1 with n = 40

Answer 24

oops ok to find the 4th term you need

\[a_{n} = a_{1} \times r^{n - 1}\]

so you know n, r and a1

just substitute and calculate

Answer 25

ooops 40th

Answer 26

2^40*3^39?

Answer 27

well a1 = 2 and r = -6 and n = 40

Answer 28

Im so confused!

Answer 29

How would I show it in simplified terms?

Answer 30

\[a_{40} = 2 \times (-6)^{40 - 1}\]

just calculate it out

Answer 31

I did, but the number is so big, how can I show it in simplified form like the multiple choice options from first question?

Answer 32

well you index solution is correct

Answer 33

???

Answer 34

you wrote

2^40 * 3^39

Answer 35

Oh awesome thanks!