HELP! Find the 11th term in the geometric sequence in which a3 is 24 and a5 is 96

a₁₁ = 6144

Step-by-step explanation:

The n th term of a geometric sequence is

= a₁

where a₁ is the first term and r the common ratio

Given a₃ = 24 and a₅ = 96 , then

a₁r² = 24 → (1)

a₁ = 96 → (2)

Divide (2) by (1)

= , that is

r² = 4 , thus

r = 2

substitute r = 2 into (1)

4a₁ = 24 ( divide both sides by 4 )

a₁ = 6

Thus

a₁₁ = 6 × = 6 × 1024 = 6144

the simplified form is

step-by-step explanation:

we want to simplify the expression,

let us change the middle bar to a normal division sign to obtain,

we multiply the first fraction by the reciprocal of the second fraction to obtain,

we factor to obtain,

we cancel the common factors to get,

we simplify to get,

the correct answer is b