The general term for the sequence 2, 4, 8, 16, 32, . . . is

Solution:

The given sequence is 2, 4, 8, 16, 32, ….

First we have to determine the common ratio and check if they are equal

r₁ = 4/2 = 2

r₂ = 8/4 = 2

r₃ = 16/8 = 2

r₄ = 32/16 = 2

As r₁ = r₂ = r₃ = r₄ it is a geometric sequence

We know that the formula which can be used is

a_n = a₁ r^{n - 1}

r = 2

Consider number of terms = n

a₁ = 2

Substituting the values in the formula

a_n = 2 (2)^{n - 1}

It can be written as

a_n = 2¹.(2)^{n - 1}

a_n = (2)^{n - 1 + 1}

a_n = 2ⁿ

Therefore, the general term is a_n = 2ⁿ.

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The general term for the sequence 2, 4, 8, 16, 32, . . . is

Summary:

The general term for the sequence 2, 4, 8, 16, 32, . . . is a_n = 2ⁿ.