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

@bibby
@TheSaint905621

Answer 2

@ilikemath50

Answer 3

the General term of geometric sequence is
\[\large a_n=a \cdot r^{n-1}\]

\[a=3\]\[a+ar=15\]

what's r?

Answer 4

12?

Answer 5

\[3+3r=15 \]\[3r=12\]\[r=?\]

Answer 6

idk? :(

Answer 7

@ilovebmth1234

Answer 8

@PaxPolaris you still there?

Answer 9

r =4

now that we have both first term and common ratio we can find the sum of the first 6 terms...

Answer 10

\[\large {S_6=a+ar+ar^2+ar^3+ar^4+ar^5\\ \ \ \ \ \ = a \left( 1+r+r^2+r^3+r^4+r^5 \right)}\]...

Answer 11

\[\Large \therefore S_6=\color{green}{a \cdot {r^6-1\over r-1}}\]

Answer 12

? none of the choices seems right ?

Answer 13

agreed but one of them is the answer and I have no idea what it is

Answer 14

the answer is 4096

Answer 15

the answer is\[\large \cancel3\cdot {4^6-1 \over \cancel{4-1}}=4096 -1 = 4095\]

it's not 4096

Answer 16

yeah ik i got 4095 but she s my sister and she put the 4096 and it was right i did it all on paper infront of her so both of us are right ha

Answer 17

4096 was right in plato