Question

In a sequence if \[{S_n}\] is the sum of first n terms and \[{S_{n - 1}}\] is the sum of first n-1 terms then the \[{n^{th}}\] term is
A. \[{S_{n - 2}}\]
B.\[{S_n} - {S_{n - 1}}\]
C.\[{S_{n + 1}} - {S_n}\]
D.\[{S_{n + 1}} - {S_{n - 1}}\]

Answer 1

Hint: We are given with the sum of first n terms and sum of first n-1 terms. There is difference of only one term in the given terms. When we need to find the \[{n^{th}}\] term we will just subtract the sum of n terms from the sum of n-1 terms. This will directly give the value of \[{n^{th}}\] term simply.

Complete step by step solution:
Given that \[{S_n}\] is the sum of first n terms.
Also given that \[{S_{n - 1}}\] is the sum of first n-1 terms
Now in order to find the last term of the series or \[{n^{th}}\] simply we will subtract the sums from each other.
\[{n^{th}}\] terms is given by \[{S_n} - {S_{n - 1}}\]
This is the only solution. So option B is the correct solution.
So, the correct answer is “Option B”.

Note: Note that the option so chosen is the only correct option. We will check for other options also.
See in option A; it is just a sum of n-2 terms that is leaving last two terms.
Next is option C; it gives the difference between sum of n terms and n+1 terms. So their difference will give you the \[n + {1^{th}}\] term and not the required.
Last is option D; it gives the difference between sum of \[n + 1\& n - 1\] terms and that will not give the \[{n^{th}}\] term