If the differences of successive terms of a series are in A.P.and G.P - Practice Questions & MCQ

If the differences of successive terms of a series are in  AP

If the differences of successive terms of a series are in A.P., we can find the $\mathrm{n}^{\text {th }}$ term of the series by the following steps :

Step 1- Denote the $n^{\text {th }}$ term by $T_n$ and the sum of the series up to $n$ terms by $S_n$.
Step 2- Rewrite the given series with each term shifted by one place to the right.
Step 3- Now, subtract the second expression of $S_n$ from the first expression to obtain the general term $\mathrm{T}_{\mathrm{n}}$

After getting the nth term, we can get the sum by applying summation to it.

If the differences of successive terms of a series are in  G.P

If the differences of successive terms of a series are in G.P., we can find the $\mathrm{n}^{\text {th }}$ term of the series by the following steps :

Step 1- Denote the $n$th term by $T_n$ and the sum of the series up to $n$ terms by $S_n$.

Step 2- Rewrite the given series with each term shifted by one place to the right.
Step 3- Now, subtract the second expression of $S_n$ from the first expression to obtain the general term $T_n$

After getting the general term $T_n$ applies summation on it to get a sum of n terms.