Question

Q.2-How many termsof AP 24,21 18, --- must be taken so that their sum is 78 ?​

Answer 1

Given,,,,,,

24,21,18,...... are in AP

a= 21,,d= 21-24= -3

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

=> 78 = n/2 [2×24 +(n-1) (-3)]

=> 156 = [48 - 3n + 3 ]

=> 156 = n [ 51-3n]

=> 3n² - 51n + 156 = 0

=> 3n² - 12n - 39n + 156 = 0

=> 3n(n-4) - 39(n-4) = 0

=> ( n-4) (3n-39)=0

Therefore,,,,

n = 4,,,,,n = 39/3= 13

When n = 4,,,,S4 =4/2 [4×24+(13-1)(-3) = 13/2[48-36] = 13/2 × 12 = 78

Hence ,,,,number of n terms are:- 4 or 13 ......

Hope it will help you,,,

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