Q19 of 202 Page 9

In an A.P. if the first term is 22, the common difference is – 4 and the sum to n terms is 64, find n.

a = 22, d = -4

S_n = 64

64 = (2a + (n – 1) d)

n [44 – (n – 1)4] = 128

n (44 – 4n + 4) = 128

48n – 4n² = 128

n² – 12n + 32 = 0

n² – 8n – 4n + 32 = 0

(n – 8) (n – 4) = 0

n = 8 or n = 4

Find the sum of all even integers between 101 and 999.

Find the sum of all integers between 100 and 550, which are multiples of 9.

In an A.P. If the 5^th and 12^th terms are 30 and 65 respectively, what is the sum of first 20 terms?

Find the sum of the first

(i) 11 terms of the A.P :

(ii) 13 terms of the A.P :

(iii) 51 terms of the A.P. whose second term is 2 and fourth term is 8.