If the sum of n terms of an A.P is given by $S_n = n^2 + n$, then the common difference of the A.P is
- 4
- 1
- 2
- 6
The Correct Option is C
Solution and Explanation
$S _{1}=1+1=2= T _{1}$
$S _{2}=2^{2}+2=6= T _{1}+ T _{2}$
$\therefore T _{2}= S _{2}- S _{1}=4$
Common difference, $d = T _{2}- T _{1}$
$=4-2$
$=2$
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Concepts Used:
Arithmetic Progression
Arithmetic Progression (AP) is a mathematical series in which the difference between any two subsequent numbers is a fixed value.
For example, the natural number sequence 1, 2, 3, 4, 5, 6,... is an AP because the difference between two consecutive terms (say 1 and 2) is equal to one (2 -1). Even when dealing with odd and even numbers, the common difference between two consecutive words will be equal to 2.
In simpler words, an arithmetic progression is a collection of integers where each term is resulted by adding a fixed number to the preceding term apart from the first term.
For eg:- 4,6,8,10,12,14,16
We can notice Arithmetic Progression in our day-to-day lives too, for eg:- the number of days in a week, stacking chairs, etc.
Read More: Sum of First N Terms of an AP