Question

The sum of the first 55 terms of an A.P. is 3300. Find the 28^th term.

Answer 1

We know that the sum of n terms of an A.P. is $S_n=\frac{n}{2}\left[2a+(n-1)d\right]$.
Also,
$S_{55}=3300$

Thus, we have:
$$\begin{gathered} \frac{55}{2}\left[2a+(55-1)d\right]=3300 \\ \left[2a+54d\right]=\frac{3300\times 2}{55} \\ 2\left[a+27d\right]=120 \\ a+27d=\frac{120}{2}=60...\left(1\right) \end{gathered}$$

Also,
We know that the n^th term of an A.P. is t_n = a + (n – 1)d.
Thus, we have:
t₂₈ = a + (28 – 1)d = a +27d
From equation (1), we get:
t₂₈ = 60