Question

Given the sequence:1,-1/3,1/9,-1/27,... Find

a) the fifteenth term.
b) the sum of the 5th term to be 10th term​

Answer 1

We can find the following pattern:

`a_1 = 1 = (-1)^0\cdot(1)/(3^0)`

`a_2 = -(1)/(3) = (-1)^1\cdot(1)/(3^1)`

`a_3 = (1)/(9) = (-1)^2\cdot(1)/(3^2)`

`a_4 = (1)/(27) = (-1)^3\cdot(1)/(3^3)`

We can deduce the generic rule

`a_n = (-1)^(n-1)\cdot(1)/(3^(n-1))`

And thus

`a_(15) = (-1)^(14)\cdot(1)/(3^(14))`

With this rule, you can compute the 5th, 6th, 7th, 8th, 9th and 10th element and sum them.