Question

The first 2 terms of a geometric sequence are √5 and 5 respectively. Find the fifth term in the sequence.​

Answer 1

Answer: the fifth term in the sequence is 25√5

Explanation:

b₁=√5 b₂=5 b₅=?

Denominator of the geometric sequence q is:

`\displaystyle\\q=(b_2)/(b_1) \\\\q=(5)/(√(5) ) \\\\q=(5(√(5)) )/(√(5)(√(5)) ) \\\\q=(5(√(5)) )/(5) \\\\q=√(5)`

b₅=b₁*qⁿ⁻¹

b₅=√5(√5)⁵⁻¹

b₅=√5(√5)⁴

b₅=√5(5)²

b₅=25√5