Question

Show that the sum of an A.P. whose first term is p, the second term is q and the last term. (p+r)(q+r-2p) is r, is equal to Z(q-p)​

Answer 1

Answer:

First term =a

second term =b Last term =c

Difference d=b−a

In an AP,nth term Tn=a+(n−1)d

                                        =a+(n−1)(b−a)

c=a+(n−1)(b−a)

∴c−a=(n−1)(b−a)

∴n−1=(b−a)(c−a)

∴n=b−ac−a+1

Sum of n numbers =n/2 ( first term+last term)

=n/2(a+c)

=2(b−ac−a+1)(a+c)

=2(b−a)(c−a+b−a)(a+c)

=2(b−a)(a+c)(b+c−2a)

Step-by-step explanation:

I hope this will help you