Q. 304.2( 4 Votes )

The 5th and 15th terms of an A.P. are 13 and - 17 respectively. Find the sum of first 21 terms of the A.P.

Answer :

Given: a5 = 13 and a15 = -17 and n = 21


We know that,


a5 = a + 4d = 13 …(i)


and a15 = a + 14d = -17 …(ii)


Solving the linear equations (i) and (ii), we get


a + 4d – a – 14d = 13 – (-17)


-10d = 13 + 17


-10d = 30


d = -3


Putting the value of d in eq. (i), we get


a + 4(-3) = 13


a = 13 + 12 = 25


Now, we have to find the sum of first 21 terms.





S21 = 21 [25 + 10 × (-3)]


S21 = 21 [-5]


S21 =-105


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