Question

pls ãñs....diz ques.....​

Answer 1

Step-by-step explanation:

We get double answer because in both cases ie; when n=18 and n=19 ..we get the sum equal to 513.

Hope it helps...!! :)

Answer 2

Step-by-step explanation:

a=54 d=-3 sum = 513

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

$513 = \frac{n}{2} (2(54) + (n - 1)( - 3)) \\ 513 = \frac{n}{2} (108 + ( - 3n + 3)) \\ 513 = \frac{n}{2} (108 - 3n + 3) \\ 513 = \frac{n}{2} (111 - 3n) \\ 513 \times 2 = 111n - 3 {n}^{2} \\ 3 {n}^{2} - 111n + 1026 = 0 \\ 3( {n}^{2} - 37n + 342) = 0 \\ {n}^{2} - 37n + 342 = 0 \\ {n}^{2} - 19n - 18n + 342 = 0 \\ n(n - 19) - 18(n - 19) = 0 \\ (n - 18)(n - 19) = 0 \\ n - 18 = 0 \: \: \: \: n - 19 = 0 \\ n = 18 \: \: \: \: \: n = 19$

as the common difference is negative we get double answer.

sum of 18 terms and sum of 19 terms is 513

hope you get your answer