Answers

2015-11-29T14:11:28+05:30
Given AP : 24, 21, 18,....
a = 24
d = 21-24 = -3
Sn = 78
n = ?
Sn = n/2 [ 2a + (n-1)d]
⇒78 = n/2[ 2(24) + (n-1)(-3)
⇒78×2 = n[ 48 - 3n + 3]
⇒156 = n[51 - 3n]
⇒156 = 51n -3n²
⇒3n² - 51n + 156 = 0
⇒3[ n² - 17n + 52] = 0
⇒n² - 17n + 52 = 0
⇒n² - 13n - 4n + 52 = 0
⇒n( n-13) - 4(n-13) = 0 
⇒(n-13) (n-4) = 0
⇒(n - 13) = 0   or  (n-4) = 0 
⇒n = 13     or    n = 4
Therefore 13 or 4 terms must be taken so that their sum is 78
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