Question

Find the number of terms in an AP in which the middle term is 50 & sum is 450.

Answer 1

Number of terms is 9 for the given A.P.

Step-by-step explanation:

Given,middle term = 50,Sum of all terms = 450.

Let the first term be "a" and last term be "l".

Since,$middle\ term = \frac{a+l}{2}$

According to question,

$\frac{a+l}{2} = 50$

Also,Sum of n terms

$S_n = n(\frac{a+l}{2})$ ,where n=number of terms

$450 = n\times 50$

$\frac{450}{50} = n$

n = 9

Hence,the number of terms in thegiven A.P is 9.