Question

FIND THE NUMBER OF TERMS OF THE A.P 54,51,48.........SO THAT THEIR SUM IS 513

Answer 1

Solution:-
Given : a = 54, d = - 3 and Sn = 513
Sn = n/2 {2a + (n - 1)d}
513 = n/2 {2*54 + (n - 1) - 3}
513 = n/2 (108 - 3n + 3)
1026 = 108n - 3n² + 3n
3n² - 111n + 1026 = 0   Dividing it by 3, we get
n² - 37n + 342 = 0
n² - 18n - 19n + 342 = 0
n(n - 18) - 19(n - 18)
(n - 18) (n - 19) = 0
n = 18 or n = 19
Therefore, the number of terms of the given AP may be 18 or 19
Answer.

Answer 2

Sry my Hnadwrinting is not good but u can understand..