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.