determine the common difference of an A.P. whose sum of n terms is an^2+bn
Answers
Answered by
9
Sn = an^2 + bn
An = Sn - Sn-1
___________________________
Sn-1 = a(n-1)^2 + b(n-1)
= a(n^2-2n+1) + bn -b
= an^2 - 2an + a + bn - b
___________________________
An = Sn - Sn-1
》an^2 + bn - an^2 + 2an - a - bn + b
》2an - a + b
__________________________
If n = 1
a1 》2a - a + b
If n = 2
a2 》 4a - a + b
》d = a2 - a1
= 4a - a + b - 2a + a - b
= 2a
》Hence common difference is 2a
☺ Hope this Helps ☺
An = Sn - Sn-1
___________________________
Sn-1 = a(n-1)^2 + b(n-1)
= a(n^2-2n+1) + bn -b
= an^2 - 2an + a + bn - b
___________________________
An = Sn - Sn-1
》an^2 + bn - an^2 + 2an - a - bn + b
》2an - a + b
__________________________
If n = 1
a1 》2a - a + b
If n = 2
a2 》 4a - a + b
》d = a2 - a1
= 4a - a + b - 2a + a - b
= 2a
》Hence common difference is 2a
☺ Hope this Helps ☺
nitthesh7:
If u find it as most helpful pls mark it as brainliest
Answered by
1
Answer:
2a
Step-by-step explanation:
Attachments:
Similar questions