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10th CBSE math solution for exercise 5.3 part 6

(6)
The first and last term of an AP are 17 and 350 respectively.If the
common difference is 9, how many terms are there and what is their sum?

Solution:

a = 17 l = 350 d = 9

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

S n= (n/2) [2 (17) + (n - 1) 9]

= (n/2) [34 + 9 n - 9]

= (n/2) [25 + 9 n] ----(1)

Sn= (n/2)[a + l]

= (n/2)[17 + 350] ------(2)

(1) = (2)

(n/2) [25 + 9 n] = (n/2)[17 + 350]

25 + 9 n = 17 + 350

9 n = 367 - 25

9 n = 342

n = 342/9

n = 38

38 terms are needed.

S₃₈ = (38/2)[17 + 350]

= 19 [367]

= 6973

(7) The sum of first 22 terms of an AP in which d = 7and 22nd term is 149.