Question

If the sum of first $$p$$ terms of an A.P. is $$ap^{2} + bp$$, then its common difference is ______.

Options

• $$a$$

• $$3a + b$$

• $$a + b$$

• $$2a$$

Answer 1

If the sum of first $$p$$ terms of an A.P. is $$ap^{2} + bp$$, then its common difference is 2a.

Explanation:

$$\mathrm{T}_{p} = \mathrm{S}_{p} - \mathrm{S}_{p - 1} = 2ap +(b - a)$$, so the common difference is $$2a$$.