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

2
by shivam2000

2015-03-13T13:03:58+05:30

### This Is a Certified Answer

Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.
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
2015-03-13T13:59:01+05:30

### This Is a Certified Answer

Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.
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