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


is equal to one fourth of the sum of the next five terms, then find the 20th 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 Sn=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 .

 

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