which of the following can be nth term of an ap 4/n+2, 4n+5, 2n^2+3, n^2-5n with reason briefly
Answers
Given:
Series with a notation of the n term 4/n+2, 4n+5, 2n^2+3, n^2-5n
To find:
Which of the given term will be the nth term of the AP.
Solution:
1) By putting the value of n as 1, 2, 3 and so on we get the series:
Series for 4/n+2:
- 4/3, 4/4, 4/5, 4/6, ............
the common difference for the terms:
- -1/3, -1/5 (which is not same)
Series for 4n+5
- 9, 13, 17, 21,...........
The common difference for the terms :
- 4, 4, 4, 4............. ( same for all terms)
Series for 2n^2+3
- 5, 11, 21, 35..........
The common difference for the terms :
- 6, 10, 14, ........... ( different)
Series for n^2-5n
- -4, -6, -6,.........
The common difference for the terms :
- -2, 0,.....(different)
Series for 4n+5 can be the nth term of an AP.
Given : (1) 4/n+2 (2) 4n + 5 (3) 2n^2 + 3 (4) n^2– 5n
To find : Which of the given terms can be the nth term of an A.P
Solution :
Common difference of an AP = aₙ₊₁ - aₙ
Common difference should not depend upon n for an AP as its fixed and independent of n
Lets check each
4/n+2
d = 4/(n + 3) - 4/(n + 2)
=> d = (4n + 8 - 4n - 12)/(n+3)(n+2)
=> d = -4/(n+3)(n+2)
dependent upon n
Hence can not be an AP
4n + 5
d = 4(n+1) + 5 - (4n + 5)
=> d = 4
hence this can be an AP
hence 4n + 5 can be nth term of an AP
2n² + 3
d = 2(n+1)² + 3 - (2n² + 3)
=> d = 2n² + 4n + 2 + 3 - 2n² - 3
=> d = 4n + 2
Dependent upon n
can not be an AP
n² - 5n
=> d = (n+1)² -5(n+1) - (n² - 5n)
=> d = n² + 2n + 1 - 5n - 5 -n² + 5n
=> d = 2n - 4
Dependent upon n
can not be an AP
4n + 5 can be the nth term of an AP
Learn more:
the seventeenth term of an ap is 5 morethan twice its eighteenth ...
https://brainly.in/question/8045489
if mth term of an A.P.is n and nth term is m, show that (m+n)th term ...
https://brainly.in/question/1085792