Question

How many terms of the AP : 24 + 21 + 18 + 15 .... be taken continuously , so that their sum is -351

Answer 1

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

Answer 2

F=24
D= 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