Question

6. If the nth term of an Ap. is pn+q
find its common difference​

Answer 1

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Answer 2

The common difference of AP is p.

Step-by-step explanation:

It has been given that the nth term of an AP is pn +q.

Mathematically, we can write

$t_n=pn+q...(i)$

Common difference of an AP is the difference between two consecutive terms. We represent common difference as d.

Thus, we have

$d=t_2-t_1$

Substituting n = 1 in (i)

$t_1=p\cdot1+q\\\\t_1=p+q$

Substituting n = 2 in (i)

$t_2=p\cdot2+q\\\\t_2=2p+q$

Thus, common difference is given by

$d=2p+q-(p+q)\\\\d=2p+q-p-q\\\\d=p$

Therefore, the common difference of AP is p.

#Learn More:

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