Question

if the first terms of an AP is 2 and the equal to one fourth of the sum of the next five term then what is the sum of the first ten term​

Answer 1

✯)Nice one. First of all let's write all given situations. For this A.P. :-

✷)a = 2 and S5 = (S10-S5)/4

✯)Lete explain the second one. The sum of first 5 terms is S5 and sum of first 10 terms is S10. So, sum of next 5 terms ( i.e sum of 6th to 10th term ) is S10 - S5.

✷)So, from this equation we get 5S5 = S10

and Sn = n/2 ( 2a + (n-1)d )

So, S5 = 5/2( 4 + 4d )

or S5 = 2.5×4(1+d) = 10(1+d)

And S10 = 10/2( 4+ 9d ) = 5(4+9d )

So, 50(1+d) = 5(4+9d)

10 + 10d = 4 + 9d

d = -6

So, Sum of first 30 terms = S30

= 30/2(4+29d)

=15(4–174)

= 15(-170)

= -255

So, required answer is -255