Question

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

Answer 1

We can find the following pattern:

$a_1 = 1 = (-1)^0\cdot\dfrac{1}{3^0}$

$a_2 = -\dfrac{1}{3} = (-1)^1\cdot\dfrac{1}{3^1}$

$a_3 = \dfrac{1}{9} = (-1)^2\cdot\dfrac{1}{3^2}$

$a_4 = \dfrac{1}{27} = (-1)^3\cdot\dfrac{1}{3^3}$

We can deduce the generic rule

$a_n = (-1)^{n-1}\cdot\dfrac{1}{3^{n-1}}$

And thus

$a_{15} = (-1)^{14}\cdot\dfrac{1}{3^{14}}$

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