Question

How many terms of the AP : 24, 21, 18, . . . must be taken so that their sum is 78?
Can u plz explain why there are two answers??

Answer 1

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first term, a = 24

common difference, d = 21-24 = -3

let the number of terms to get sum 78 is n.

Sn = n/2 (2a +( n-1) d)

78 = n/2(48+ (-3)n + 3)

78 = n/2(51 + (-3)n)

78*2=n (51+ (-3)n)

156= 51n + -3n^2

3n^2-51n+156=0

n^2 - 17n +52 =0

n^2-13n-4n +52 =0

n(n-13)-4(n-13)=0

(n-4)(n-13) =0

n = 4,13

 

Solving the quadratic equation, we get n=4 and n=13.

So you can take either 4 terms or 13 terms to get the sum 78.

we get 2 answers because the AP of the sequence can be formed from two methods.

Answer 2

By solving the equation formed by the accordance to the question we get two value of n .