Question

A geometric series has a sum of 9,837. The common ratio is 3 and the first term is 9. How many terms are in the series?

Answer 1

https://en.wikipedia.org/wiki/Geometric_series

Answer 2

this is fun

Answer 3

to find any term in geometric sequence
\[a_n=a_1\times r^{n-1}\]
a1 = first term
r= common ratio
n = number of the term to find

Answer 4

9837 = 9 * 3^(n-1)

do you know logarithm?

Answer 5

Yeah I would know how to find it out using the equation you wrote but I dont know the number of terms there are. that is what i am trying to find

Answer 6

They give me multiple choice answers:
A. 5
B. 7
C. 9
D. 11

Answer 7

if you know how to find out, then why can't you determine the terms?

Answer 8

because the equation you wrote requires number of terms I am trying to find... lol sorry if I am being real dumb

Answer 9

\[\Large Sum = a \times \frac{ 1 - r^n }{ 1-r }\]

Answer 10

you can try plugging in and evaluate the sum

Answer 11

\[9837 = 9 \times \frac{ 1 - 3^n }{ 1-3 }\]
Solve for n.

Answer 12

@ranga she is stuck in the same predicament as before

Answer 13

you can use the choices and plug them one by one until the sum equals

Answer 14

my guess would be 7 ;)

Answer 15

I tried just pluggin them all in but for some reason none of them work...

Answer 16

try ranga's sum of series

Answer 17

http://www.regentsprep.org/Regents/math/algtrig/ATP2/GeoSeq.htm

Answer 18

is it 7????

Answer 19

\[9837 = 9 \times \frac{ 1 - 3^n }{ 1-3 } = 9 \times \frac{ 3^n - 1 }{ 3-1 } = \frac{ 9 }{ 2 } \times (3^n-1)\]\[3^n -1 = 9837 \times \frac{ 2 }{ 9 } = 2186 \\ 3^n = 2187\]

Answer 20

yes. n = 7.

Answer 21

yaaaaa even using the first formula, you'll get 7 as an estimated value

Answer 22

thank you both!!!!!!

Answer 23

something's amiss

Answer 24

Since there are just 7 terms, I can list the entire geometric series here:
9, 27, 81, 243, 729, 2187, 6561.
7 terms total.
Add them up and the sum will be 9837.