Question

If the sum of first p terms of an AP is ap2+bp, find its common difference

Answer 1

i hope this will usful to u

Answer 2

$sum \: of \: p \: tems \: in \: ap = sp \\ \\ sp = ap {}^{2} + bp \\ \\ s1= a1 {}^{2} + b1 = a +b \\ \\ s2 = a2 {}^{2} + b2 = 4a + 2b \\ \\ a1 = s1 = a + b \\ \\ a2 = s2 - s1 = 4a + 2b - (a + b) \\ \\ = 4a + 2b - a - b \\ \\ = 3a + b \\ \\ common \: difference \: = d \\ \\ d = a2 - a1 \\ \\ = 3a + b - (a + b) \\ \\ = 3a + b - a - b \\ \\ = 2a$

✌✌✌✌✌✌✌✌✌✌

#follow me