. If the first term of an A P is 2 and the sum of first term

Best Answer

Explanation: 

It is given that first term a=2 

Also, sum of first five terms =1/4 times Sum of next 5 terms.

a₁+ a₂+a₃+a₄+a₅=1/4(a₆+a₇+a₈+a₉+a₁₀)

Sum of first five terms =1/4 sum of 6th and 10th terms 

Sum of first five terms =1/4 sum of 10th - sum of first five terms

⇒S₅=1/4(s₁₀-s₅)

⇒4s₅=s₁₀-s₅

⇒5s₅=s₁₀…(1)

We know that sum of n terms of an A.P S_n=n/2(2a+(n-1)d)

Put a=2,n=5 

S₁₀=10/2(2×2+(10-1)d)

=20+45d

From eq(1) 

5S₅=S₁₀

⇒5(10+10d)=20+45d

⇒5d-30

⇒D=6

20th term of  an A.P =2+(20-1)(-6)=-112 

Final Answer: 

Hence, the 20th term of an A.P is-112 .