Question

The first term of a geometric series is 3, and the sum of the first term and the second term is 15. What is the sum of the first six terms?
1,023

3,906

4,096

11,718

Answer 1

Geometric series are defined by each term being the previous term multiplied by the same constant. If the first term is 3 then the second will be 3y and the third will be 3(3y) etc. If the sum of the first two terms is 15 then you know that 3 + 3y = 15 and you can find y to be 4. That means to find the next term in the sequence just need to multiply by 4. You could then just find the first 6 terms and add them up as it's not that many but there is a formula for the sum of a geometric series given by \[\frac{ a(1-r ^{n}) }{ 1-r }\] Where a is the first term, 3 in this case, and r is the multiplier, in this case 4 and n is the number of terms. So just stick 3, 4 and 6 in to the equation and you're golden.

Answer 2

yeah but where are you getting the four from? @alrightatmaths

Answer 3

That was from 3 + 3y = 15. Cause the first term is 3 and the second term will be 3 multiplied by something, which I've called y and then 3 + 3y = 15 as the question tells us. Taking 3 from both sides gives 3y = 12 and dividing by 3 gives y=4. So the number you multiply by each time is 4.

Answer 4

ok thats helpful thanks @alrightatmaths

Answer 5

No problem

Answer 6

do i plug 6 in into a in the equation? @alrightatmaths

Answer 7

No, a is the first term of the sequence, which is 3 here. 6 is the number of terms that you're adding up, which is n in the formula.

Answer 8

and 4 is R right

Answer 9

@alrightatmaths

Answer 10

would it be 4096??? @alrightatmaths