The seconds term of a geometric series is 4 while the fourth term is 16….

Explanation

T₂ = 4, T₄ = 16

T_x = ar^n-1

T₂ = ar^2-1 = 4 i.e. ar³ = 16, i.e. ar = 4

T₄ = ar^4-1

therefore, \(\frac{T_4}{T_r}\) = \(\frac{ar^3}{ar}\) = \(\frac{16}{4}\)

r² = 4 and r = 2

but ar = 4

a = \(\frac{4}{r}\) = \(\frac{4}{2}\)

a = 2

Sⁿ = \(\frac{a(r^n - 1)}{r - 1}\)

S⁵ = \(\frac{2(2^5 - 1)}{2 - 1}\)

= \(\frac{2(32 - 1)}{2 - 1}\)

= 2(31)

= 62

There is an explanation video available .