Question

If 12th term of an AP is twice the sum of its four terms is 24. What is the sum of iys first 10 tems

Answer 1

Answer:

183/25.

Step-by-step explanation:

For the 12th term we have T12=a+11d which is equal to twice of the sum of four terms so, a+11d=2[2(2a+3d)] which on solving we get that a+11d=8a+12d or 7a+d=0.

Now, from the question we have 2(2a+3d)=24 which again on solving we have a+3d=12. Now, solving the two equations simultaneously we have to multiply the first equation by 3 and then subtracting the two equations we will get the value of a=-3/5 and then putting the value of a in the first equation we will get d=21/5.

So, the summation of 10 terms will be S(10)=10/2[2(-3/5)+9(21/5)] which on solving we will get 183/25.