Question

if (m+2)th term of an AP is (m+2)^2-m^2, then find the common difference ?

plz give answer with method

Answer 1

I think this clippings may help you

Answer 2

Answer:

The common difference, d=$\frac{4m+4-a}{m+1}$

Step-by-step explanation:

Let a be the first term of a given AP and d be the common difference of given AP.

We have to find the value of common difference d

We are given that the $(m+2)^{th}$term of an AP is $(m+2)^2-m^2$

$a_{m+2}=(m+2)^2-m^2$

We are using formula

$a_n=a+(n-1)d$

Where$a_n=n^{th}$ term of an AP

n=Total number of terms in an AP

d= Common difference

a= First term of an AP

Applying this formula we get the value of common difference

Therefore, $(m+2)^2-m^2=a+(m+2-1)d$

$(m+2-m)(m+2+m)=a+(m+1)d$

Using identity :$a^2-b^2=(a+b)(a-b)$

$(2m+2)\times2=a+(m+1)d$

$4m+4-a=(m+1)d$

$d=\frac{4m+4-a}{m+1}$

Hence, the common difference, d=$\frac{4m+4-a}{m+1}$