Question

21 x
Sn: 735
4) If the nth term of AP is (2n+1), find the sum of first n
terms of the AP
->​

Answer 1

Answer:

Sum of first n terms of an AP having its first term as a and common difference as d is given by

S = (n/2)*[2a+(n-1)d]

Sum of first 21 terms of the AP is 28. This gives 28 = (21/2)[2a+20d]. Or, 28 = 21a+210d. This implies 3a+30d = 4.

Sum of first 28 terms of the same AP is 21. This gives 21 = (28/2)[2a+27d]. Or, 21 = 28a+378d. This implies 4a+54d = 3.

Solving the two equations 3a + 30d = 4 and 4a + 54d = 3 as simultaneous equations in the two unknowns a and d, we get

a=3 and d=(-1/6).

The AP is thus 3, 17/6, 8/3, 5/2, 7/3,13/6,2,11/6,……

We know that nth term of AP with the first term a and common difference d is a+(n-1)d

Hence, 19th term of this AP with first term as 3 and common difference as (-1/6) will be 3 + (19–1)(-1/6) = 3 + 18 (-1/6) = 0.

Hence 19 th term of the AP will be zero.

Sum of the preceding terms is equal to sum of first 18 terms of the AP. This is given by

S = (n/2)[2a + (n-1)d] = (18/2)[2(3) + 17(-1/6)] = 9[6–17/6] = 9[19/6] =57/2.