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in Arithmetic Progression by (56.3k points)

How many terms of the AP : 24, 21, 18, ... must be taken so that their sum is 78?

1 Answer

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Best answer

Given A.P. 

24, 21, 18,..... 

First term = 24 = a 

and common difference = – 3 = d ...(i) 

Let no. of terms is n. 

Sum of n terms = \(\frac{n}{2} [2a + (n - 1)d]\)

According to question

\(78 = \frac{n}{2} [2 \times 24 - 3 \times (n -1)]\) [from (i) and given]

\(78 = \frac{n}{2} [51- 3n]\)

n2 – 17n + 52 = 0

n2 – 13n – 4n + 52 = 0 

n(n – 13) – 4 (n – 13) = 0 

(n – 13) (n – 4) = 0 

n = 13, 4 

For first 4 terms and first 13 terms in both case we get sum 78.

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