Question

the 5th term of a geometric sequence is 144 and the 10th term is 4608. find the first term and common difference

Answer 1

first term:9

common ratio: 2

Explanation:

aₙ = a₁*rⁿ⁻¹

a₅ = a₁*r⁵⁻¹ = a₁*r⁴ = 144 ... (1)

a₁₀ = a₁*r¹⁰⁻¹ = a₁*r⁹ = 4608 ... (2)

(2)÷(1) r⁵ = 32

r = 2

a₁ = 144 / 2⁴ = 9

Answer 2

First term = 9.

Common ratio = 2.

Explanation:

A geometric sequence has a common ratio r.

If the first term is a:

10th term = ar^9 and 5th term is ar^4

so 1th term / 5th term = r^5

So 4608/144 = r^5

r^5 = 32

so r = 2.

Substituting for r in the 5th term:

a(2)^4 = 144

a = 144 / 16

a = 9.