Question

Can someone show how to solve this

The sum of the first two terms of a geometric series is 12 and the sun of the first three terms is 62. Find the series (the first 3 terms in the series)

Answer 1

Do u have the answers in your text book?

Answer 2

Is the first term in decimal form?

Answer 3

I found how its done if you're still there

Answer 4

can you please show how to solve

Answer 5

Do you have an email so that I send it as a photo to you

Answer 6

do you mind uploading teh photo here?

Answer 7

definition of geometric series a(n+1) = k a(n)

start
a(1) + k a(1) = 12
next
a(1) + k a(1) + k^2 a(1) = 62

divide the second equation by the first, so that a(1) drops out and you have only k terms

[1 + k + k^2] / (1 + k) = 62/12 = 5.16

multiply both sides by (1 + k), then put into standard quadratic form
and solve quadratic equation for k.

Having gotten k, go back to first equation to get a(1).

Then: a(1) you have and a(2) = k a(1) and a(3) = k^2 a(2), so you have first three terms.

Messy but doable. The rest is yours.

Answer 8

How can I upload it for you?

Answer 9

Nooo...I am going to bed too soon. You can do this, I think.

Answer 10

I've solved it already but in a different way

Answer 11

Congratulations!

Answer 12

Less messy than yours :)

Answer 13

Double the congratulations!

Answer 14

Thank you Douglas I'm gonna give u a medal for that ;)

Answer 15

I go to bed with a smile. Gracious of you. I reciprocate.

Answer 16

Sweet dreams my friend

Answer 17

@waheguru do you still want my version?

Answer 18

@Chad123 Im sorry I was gone but yet I would apperichate your solution you can upload it using the attach file button.

Answer 19

if you have any questions let me know

Answer 20

Thanks alot

Answer 21

@Chad123 I understand how you did it with a + a*r and so on but what if the question have the sum of 30 terms then it wouild not be logical to do that all the way to 30, is there another way to solve these sort of questions?

Answer 22

If you look at the top right hand corner you will find a formula xn=ar^n-1. Since you have the values of a and r you'll be able to find any term represented by the variable n

Answer 23

Sorry that's if you want to find the value of each term but if you want to know the sum of 30 terms or any number of terms you simply use the formula a(1-r^n)/1-r

Answer 24

This only works for geometric sequences