Mathematics
If the sum of first p terms of an A.P. is ap2 + bp, then its common difference is :
a
3a + b
a + b
2a
Answer
Given,
⇒ Sp = ap2 + bp
⇒ Tp = Sp - Sp - 1
= ap2 + bp - [a(p - 1)2 + b(p - 1)]
= ap2 + bp - [a(p2 - 2p + 1) + bp - b]
= ap2 + bp - [ap2 - 2ap + a + bp - b]
= ap2 + bp - ap2 + 2ap - a - bp + b
= 2ap - a + b.
d = Tp - Tp - 1
= 2ap - a + b - [2a(p - 1) - a + b]
= 2ap - a + b - [2ap - 2a - a + b]
= 2ap - a + b - 2ap + 2a + a - b
= 2a.
Hence, option 4 is the correct option.
Related Questions
The 5th term of an A.P. is −3 and its common difference is −4. The sum of its first 10 terms is :
−50
−40
−60
−30
The 7th term of an A.P. is −1 and its 16th term is 17. The nth term of the A.P. is :
(3n + 12)
(2n − 5)
(3n + 5)
(2n − 15)
The first three terms of an A.P. are 3y − 1, 3y + 5 and 5y + 1 respectively. Then, the value of y is :
1
5
8
3