Question

which term of the GP 5, 10, 20 40,... is5120​

Answer 1

Answer:

• 11th term.

Step-by-step explanation:

Given

• G.P : 5 , 10 , 20 , 40 , ..

To find

• Which term of the G.P is 5120 ?

Solution

Here :

• a (first term) = 5
• r (common ratio) = 10/5 = 2

Let its nth term be 5120.

Then Tₙ = 5120

We know: general term or nth term of an G.P :

• arⁿ ⁻ ¹

Substituting we get :

• (5)(2)ⁿ ⁻ ¹ = 5120
• (2)ⁿ ⁻ ¹ = 5120/5
• (2)ⁿ ⁻ ¹ = 1024
• (2)ⁿ ⁻ ¹ = (2)¹⁰
• n - 1 = 10
• n = 10 + 1
• n = 11

Hence, the 11th term of the GP is 5120.