Question

if m+2 term of an AP is m+2square -2square then its common difference ​

Answer 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}(m+2)

th

term of an AP is (m+2)^2-m^2(m+2)

2

−m

2

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

m+2

=(m+2)

2

−m

2

We are using formula

a_n=a+(n-1)da

n

=a+(n−1)d

Wherea_n=n^{th}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)

2

−m

2

=a+(m+2−1)d

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

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

2

−b

2

=(a+b)(a−b)

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

4m+4-a=(m+1)d4m+4−a=(m+1)d

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

m+1

4m+4−a

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

m+1

4m+4−a