Question

Write down the first five terms of the geometric progression which has first term 1 and common ratio 4.

Answer 1

In the given G.P., we have the first term, i.e., a = 1, and the common ratio, i.e., r = 4.
We know that the n^th term of the G.P. is t_n = ar^{n – 1.}
To find the first five terms of the given G.P., we need to take n = 1, 2, 3, 4 and 5.
For n = 1, we get:
t₁ = (1)(4)^{1 – 1}
$\Rightarrow$ t₁ = (1)(4)⁰ = 1

For n = 2, we get:
t₂ = (1)(4)^{2 – 1}
$\Rightarrow$ t₂ = (1)(4)¹ = 1 × 4 = 4

For n = 3, we get:
t₃ = (1)(4)^{3 – 1}
$\Rightarrow$ t₃ = (1)(4)² = 1 × 16 = 16

For n = 4, we get:
t₄ = (1)(4)^{4 – 1}
$\Rightarrow$ t₄ = (1)(4)³ = 1 × 64 = 64

For n = 5, we get:
t₅= (1)(4)^{5 – 1}
$\Rightarrow$ t₅ = (1)(4)⁴ = 1 × 256 = 256

Thus, the first five terms of the given G.P. are 1, 4, 16, 64 and 256.