Question

Find the sum of the first 10 terms of the following sequence. Round to the nearest hundredth if necessary.19, -95, 475,...

Answer 1

-3,092,446

Step-by-step explanation

We want to find the sum of the first 10 terms of the geometric sequence given:

`19,-95,475`

The common ratio of the sequence is -5 and the first term is 19.

The formula for the sum of the first n terms of a geometric sequence is:

`S=(a_1(1-r^n))/(1-r)`

Therefore, for the given sequence:

`\begin{gathered} S=(19(1-(-5)^(10)))/(1-(-5)) \\ S=(19(1-9765625))/(1+5)=(19(-9765624))/(6) \\ S=-3092446 \end{gathered}`

That is the answer.