Question

What is the sum of the first 7 terms of the sequence `10xx(-2)^(i-1)` ?

Answer 1

430

Explanation:

The sum of the first n terms of a geometric series with first term `a_1` and common ratio r is given by:

`sum_(i=1)^n = [a_1(1-r^n)]/(1-r)`

In this example, `n=7, a_1 = 10` and `r=-2`

Hence, `sum_(i=1)^7 = (10*(1-(-2)^7))/(1-(-2))`

`= (10*(1-(-128)))/3`

`=1290/3 = 430`