Q34 of 176 Page 8

The first and the last terms of an A.P. are 17 and 350 respectively. If the common difference is 9, how many terms are there in the A.P. and what is their sum?

Given: First term, a = 17


Last term, l = 350


common difference, d = 9


We know that,


l = a + (n – 1)d


⇒ 350 = 17 + (n – 1)9


⇒ 333 = (n – 1)9


⇒ 37 = n – 1


⇒ n = 38


So, there are 38 terms in the AP


Now, we have to find the sum of this AP




⇒ S38 = 19 [34 +37×9]


⇒ S38 = 19 [34 + 333]


⇒ S38 = 19 × 367


⇒ S38 = 6973


Hence, the sum of 38 terms is 6973.


More from this chapter

All 176 →
33

Find the sum of the first 25 terms of the A.P. whose 2nd term is 9 and 4th term is 21.

 34

If the sum of 8 terms of an A.P. is 64 and the sum of 19 terms is 361, find the sum of n terms.

 35

If a, b, c be the 1st, 3rd and nth terms respectively of an A.P., there prove that the sum to n terms is

36

If the mth term of an A.P. is and the nth term is , then prove that the sum to mn terms is , where in m n.