Question

1. the first and the last term of an ap are 17 and 350 respectively. if the common difference is 9 ,how many terms are there in their AP and what is their sum.

Answer 1

Let the first term of A.P. = a , Common difference = d

Now according to question

Sum of first 8 terms = (8/2)[2a + (8 - 1) d] {Using sum of n terms of an A.P. = (n/2)[2a + (n - 1) d]}

= 64 = 4[2a + 7d] = 2a + 7d = 64/4 (rearranging)

= 2a + 7d = 16 ...............(1)

Similarly , Sum of first 19 terms = (19/2)[2a + (19 - 1)d]

= 361 = (19/2)[2a + 18d] = 361 = (19/2) * 2 *(a + 9d) [Taking 2 common ]

= 361 = 19 [a + 9d] = a + 9d = 361/19 (rearranging)

= a + 9d = 19 .........(2)

Multiplying equation (2) by 2 we get

= 2a + 18d = 38 .........(3)

Subtracting equation (1) from equation (3) we get

2a + 18d - (2a + 7d) = 38 -16 = 2a + 18d - 2a - 7d = 22

= 11d = 22 = d = 22/11

= d = 2

Putting value of d in equation (2) we get

a + 9 (2) = 19 = a + 18 = 19

= a = 19 - 18 = a = 1

Thus sum of n terms of the series = (n/2) [2*1 + (n -1)2] = (n/2)[2 + 2n - 2] = (n/2)[2n] = n²

Answer 2

a17. a350
a+16d
a+16 *9
a=135