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if the sum of fist p terms of an AP is ap 2 +bp,find its common difference

Hi!
Here is the answer to your question.
 
Le d be the common difference of A.P.
Sp = ap2 + bp
∴ap = Sp – Sp – 1
  = (ap2 + bp) – [a (p – 1)2 + b(p – 1)
  = (ap2 + bp) – (ap2 – 2ap + a + bp – b)
  = 2ap + b – a
d = ap – ap – 1
  = [2ap + (b – a)] – [2a (p – 1) + (b – a)]
  = 2ap – 2ap + 2a
  = 2a
Thus, the common difference of A.P. is 2a
 
Cheers!

  • 9
View Full Answer

 ap = ap2 + bp

a1 = a + b

S2 = 4a + 2b

a2 = 3a + b

d = 3a + b- a - b

d = 2a

  • 3

 put p=1

S1=a+b (i.e. first term of A.P

PUT p=2

S2=4a+2b(i.e.sum of 2 term)

second term S2-S1

=4a+2b-(a+b)

=4a+2b-a-b

=3a+b

so the difference second term-first term 

=3a+b-(a+b)

=3a+b-a-b

=2a

i hope you understant 

if not u may contact me on abhiabhimehta@gmail.com

  • 4

sum of first term will be=a(1)(1)+b(1)=a+b 

sum of second term= a(2)(2)+b(2)=4a+2b

2ndterm = sum of second term - sum of first term= 4a+2b-(a+b)=3a+b

1st term =4a+2b-(3a+b)

                    = a+b

now D=second term-first term=(3a+b)-(a+b)

 =2a

  • 2
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