Question

If sn =np+1/2n(n-1)q,where sn denotes the sum of first n terms of an



a.P.,then find their common difference

Answer 1

thank you..............

Answer 2

The common difference of the AP is q.

• The sum of n terms of AP is given by $S_n = np + \frac{1}{2}n(n-1)q$ .    (Equation 1)

• Let a₁,a₂,a₃,a₄,...,$a_n$ be the given AP.

Putting n=1 in the equation

$S_1 = p + \frac{1}{2}1(1-1)q$

$S_1 = p$

• First term is represented as $a_1$.

∴ a₁ (First term)= S₁ = p

• Now , putting n=2 in the equation 1

$S_2 = 2p + \frac{1}{2}2(2-1)q$

$S_2 = 2p + q$      (Equation 2)

• Now, S₂ = first term + second term

first term + second term = 2p + q

• But first term = p

∴ p + second term = 2p + q

second term = p + q

• Now,

Common difference = Second term - first term

Common difference = p+ q - p

Common difference = q