Question

Sum of first 55 terms in an A.P. is 3300, find its 28^th term.

Answer 1

It is given that,
S₅₅ = 3300

We know that,
$$\begin{gathered} S_n=\frac{n}{2}\left(2a+\left(n-1\right)d\right) \\ {S}_{55}=\frac{55}{2}\left(2a+\left(55-1\right)d\right) \\ \Rightarrow 3300=\frac{55}{2}\left(2a+54d\right) \\ \Rightarrow \frac{3300\times 2}{55}=2\left(a+27d\right) \\ \Rightarrow 120=2\left(a+\left(28-1\right)d\right) \\ \Rightarrow 60=a+\left(28-1\right)d \\ \Rightarrow a_{28}=60 \end{gathered}$$

Hence, its 28^th term is 60.