Question

NEED AN EXPLANATION WITH ANSWER

Answer 1

Answer:

Multiply both side by r.

Step-by-step explanation:

The derivation process is explained below and you will know the answer from this derivation

S = a + ar + ar² + ........... + arⁿ ········(1)

Multiplying both side by r, we get

rS = ar + ar² + ............+ arⁿ + ar⁽ⁿ⁺¹⁾ ········(2)

Substracting (1) from (2) we get

(r-1)S = -a + ar⁽ⁿ⁺¹⁾

(r-1)S = a( rⁿ⁺¹ - 1 )

$s \: = \frac{ a({r}^{n + 1} - 1 )}{(r - 1)}$