Graph the first six terms of a sequence where a₁ = 2 and r = 4

Solution:

It is given that

a₁ = 2

r = 4

n = 6

The formula of nth term of a geometric progression is

a_n = ar^{(n - 1)}

a₁ = 2

a₂ = 2 × 4^{(2 - 1)} = 2 × 4¹ = 8

a₃ = 2 × 4^{(3 - 1)} = 2 × 4² = 32

a₄ = 2 × 4^{(4 - 1)} = 2 × 4³ = 128

a₅ = 2 × 4^{(5 - 1)} = 2 × 4⁴ = 512

a₆ = 2 × 4^{(6 - 1)} = 2 × 4⁵ = 2048

Therefore, the first six terms of a sequence are 2, 8, 32, 128, 512 and 2048.

Graph the first six terms of a sequence where a₁ = 2 and r = 4

Summary:

The first six terms of a sequence where a₁ = 2 and r = 4 are 2, 8, 32, 128, 512 and 2048.