What are the first five terms of the geometric sequence a1 = 3, an = 4 ⋅ an − 1 ?

What are the first five terms of the geometric sequence a1 = 3, an = 4 ⋅ an − 1?

Expert Solution

Consider a geometric sequence with recursive formula,

a1 = 3

an = 4 ∙an-1 ...... (1)

First term of given sequence is, a1 = 3

Substitute n = 2 and a1 = 3 in formula (1) an = 4 ∙an-1 and compute second term,

a2 = 4 ∙ a1

= 4 × 3

= 12

Substitute n = 3 and a2 = 12 in formula (1) an = 4∙an-1 and compute third term,

a3 = 4∙a2

= 4 × 12

= 48

Substitute n = 4 and a3 = 48 in formula (1) an = 4∙an-1 and compute fourth term,

a4 = 4∙a3

= 4 × 48

= 192

Substitute n = 5 and a4 = 192 in formula (1) an = 4∙an-1 and compute fifth term,

a5 = 4∙a4

= 4 × 192

= 768

Therefore, first five terms of given sequence is {3, 12, 48, 192, 768}.

Junaid answered 1 year ago

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