Question

Which term of the G.P is 5,10,20,40 .. is 2560 ?

Answer 1

Answer:

2560 is the term 10th term of the given G.P.

Step-by-step explanation:

Given :-

G.P : 5, 10, 20, 40

To find :-

Which term of the above G.P. is 2560 ?

Solution :-

Here,

First term (a) = 5

Common ratio (r) = 10/5 = 2

Now, general term of a G.P

arⁿ ⁻ ¹ = 2560

Tₙ = 2560

• 5 × 2ⁿ ⁻ ¹ = 2560
• 2ⁿ ⁻ ¹ = 2560/5
• 2ⁿ ⁻ ¹ = 512
• 2⁹ = n - 1 = 9
• n = 10

∴ 2560 is the term 10th term of the given G.P.

Answer 2

Answer:

The given G.P. has first term a=5 and the common ratio r=2. Let the nth term be 5120. Then,

a  

n

​  

=5120

ar  

n−1

=5120

5(2  

n−1

)=5120

2  

n−1

=1024

2  

n−1

=2  

10

 

n−1=10

n=11