(Q5).How many terms of the AP : 24, 21, 18, . . . must be taken so that their sum is 78?

Here, a = , d = – = –, Sn = . Let number of terms of AP is n, then we need to find n.

We know that Sn =
n
2
 [2a + (n-1)d]
So, =
n
2
 [ + (n-1)(-)] =
n
2
 [-n]

or n2 – n + = 0

or n2 – n + = 0

or (n – )(n – ) = 0

or n = or

Both values of n are admissible. So, the number of terms is either or .