Question

Arithmetic and geometric series -Find the sum of the first 50 terms of the following series, to the nearest integer.

Answer 1

Answer:

            10,450

Step-by-step explanation:

21-13=8   and   29-21=8

So this is aritmetic series where a₁ = 13, and r = 8

Sum of the first n terms:  

$S_n=\dfrac{a_1+a_n}{2}\cdot n=\dfrac{a_1+a_1+(n-1)r}{2}\cdot n=\dfrac{2a_1+(n-1)r}{2}\cdot n\\\\\\S_{50}=\dfrac{2\cdot13+(50-1)\cdot8}{2}\cdot50=(13+49\cdot4)\cdot 50=10,450$