Question

For an A.P. show that Tp + Tp+2q = 2Tp+q​

Answer 1

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Answer 2

Step-by-step explanation:

To show that: T

p

+T

p+2q

=2T

p+q

Proof :-

T

p

=a+(p−1)d where a = first term and d = common difference

T

p+2q

=a+(p+2q−1)d

∴T

p

+T

p+2q

=a+(p−1)d+a+(p+2q−1)d

=a+pd−d+a+pd+2qd−d

=2a+2pd+2qd−2d

=2(a+pd+qd−d)

=2[a+(p+q)d−d]

=2[a+(p+q−1)d]

=2T

p+q

Hence proved