Question

Can someone please help me find the sum of the first six terms of the geometric sequence for which a2 = 0.7 and a3 = 0.49 ?

Answer 1

would the answer be 7203? I don't know if this is correct but because it seems to multiply by 7's, I basically did 7 to the 6th power (7^6)

Answer 2

The common ratio is found by dividing dividing the third term by the second term:
\[r=\frac{0.49}{0.7}=0.7\]
the first term is found by dividing the second term by the common ratio:
\[a _{1}=\frac{0.7}{0.7}=1\]
The formula for the sum of n terms is
\[S _{n}=\frac{a _{1}(1-r ^{n})}{1-r}=\frac{1-0.7^{6}}{1-0.7}=you\ can\ calculate\]