The number of terms in the sequence 5, 20, 80, 320, ……, 81920 is:

Given sequence:
5, 20, 80, 320, … , 81920
Check the pattern:
20 ÷ 5 = 4
80 ÷ 20 = 4
320 ÷ 80 = 4
So, each term is multiplied by 4.
Hence, this is a Geometric Progression (GP).
First term:
a = 5
Common ratio:
r = 4
Last term:
aₙ = 81920
Formula for nth term of GP:
aₙ = a × rⁿ⁻¹
Substitute the values:
81920 = 5 × 4ⁿ⁻¹
Divide both sides by 5:
16384 = 4ⁿ⁻¹
Now,
16384 = 2¹⁴
Also,
4 = 2²
Therefore:
4ⁿ⁻¹ = (2²)ⁿ⁻¹
= 2²⁽ⁿ⁻¹⁾
So,
2²⁽ⁿ⁻¹⁾ = 2¹⁴
Equate powers:
2(n − 1) = 14
n − 1 = 7
n = 8