Question

What is the sum of the first five terms of a geometric series with a1 = 10 and r = 1/3

Answer 1

Can you write out the first 5 terms?

Answer 2

the first term is already given as 10

Answer 3

what is the second term?

Answer 4

i will help you out
these are the first five terms
\[a_1,a_1r,a_1r^2,a_1r^3,a_1r^4\]

Answer 5

where a_1=10 and r=1/3

Answer 6

so the sum is
\[a_1+a_1r+a_1r^2+a_1r^3+a_1r^4 \\ =a_1(1+r+r^2+r^3+r^4)\]

Answer 7

or you could use the formula for a sum if you so choose

Answer 8

\[a_1 \frac{1-r^5}{1-r}\]

Answer 9

what about 1/3?

Answer 10

I don't think the sum will be 1/3

Answer 11

replace the a_1's with 10
and replace the r's with 1/3
you can use the formula
or just add up those five terms I mentioned

Answer 12

\[10+10(1/3)+10(1/3)^2+10(1/3)^3+10(1/3)^4+10(1/3)^5\]

is this what you mean?
#freakles

Answer 13

well that is first 6 terms you are adding

Answer 14

you want to add the first 5 so leave the last one off