Given A.P. is 24+21+18+ ............. Sn = -351 a = 24 d = 21-24 = -3 n = ? Sn = n[2a+(n-1)d]/2 -351 = n[2*24+(n-1)*-3]/2 -702 = n[51 - 3n] 3n² - 51n -702 = 0 n² - 17n - 234 = 0 n² - 26n + 9n - 234 = 0 n(n - 26) + 9(n - 26) = 0 (n-26)(n+9) = 0 n = 26 or -9 as n can not be negative so n = 26
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Verified answer
Given A.P. is 24+21+18+ .............Sn = -351
a = 24
d = 21-24 = -3
n = ?
Sn = n[2a+(n-1)d]/2
-351 = n[2*24+(n-1)*-3]/2
-702 = n[51 - 3n]
3n² - 51n -702 = 0
n² - 17n - 234 = 0
n² - 26n + 9n - 234 = 0
n(n - 26) + 9(n - 26) = 0
(n-26)(n+9) = 0
n = 26 or -9
as n can not be negative so
n = 26
Verified answer
F=24D= 21-24= -3
N= NUMBER OF TERMS
SN= -351
-351= \frac{D}{2} N^{2}+(F- \frac{D}{2})N \\ \\
\frac{-3}{2} N^{2} +(24- \frac{-3}{2})N \\ \\
-3N ^{2} +51N= -351*2=- 702 \\ \\
DIVIDE/BY/-3 \\ \\
N ^{2} -17N=234\\
N^{2}-17N+8.5 ^{2} =234+8.5 ^{2} \\
(N-8.5) ^{2} =306.25
(N-8.5)=17.5
N=17.5+8.5
N=26