Question

if the sum of first P term of an ap is equal to the sum of first Q terms then what find the sum of The P+q term​

Answer 1

Step-by-step explanation:

see the attached photo for solution

Answer 2

Let the first term of the AP be a , & it's common difference be d . We have :

$\huge{{S}_{p} = {S}_{q}} \\\\\ \implies \frac{p}{q} (2a+(p-1)d) = \frac{q}{2} (2a+(q-1)d) \\\\\ \implies 2ap + p(p-1)d = 2aq + q(q-1)d \\\\\ \implies 2a(p-q) + ((p²-q²)-(p-q))d= 0 \\\\\ \implies 2a + (p+q-1)d=0 \\\\\ {S}_{p+q} = \frac {(p+q)}{2} (2a+(p+q-1)d) \\\\\ = \frac{(p+q)}{2} \times 0 \\\\\ = 0$