Question

What is the ${{n}^{th}}$ term of $4,8,12,16,....$ ?

Answer 1

Hint: Here in this question we have been asked to find the ${{n}^{th}}$ term of the given sequence $4,8,12,16,....$ . To answer this question we will first find the common difference between the terms of the given sequence if it follows the arithmetic progression pattern then we will use the formula for the ${{n}^{th}}$ term of an arithmetic progression.

Complete step-by-step solution:
Now considering from the question we have been asked to find the ${{n}^{th}}$ term of the given sequence $4,8,12,16,....$ .
From the basic concepts of progressions we know that the arithmetic progression is defined as a sequence consisting of terms in which successive terms have common differences between them.
By evaluating the given sequence we can say that the difference between the succeeding terms in the given sequence is common and its value is given as $\Rightarrow 8-4=12-8=4$ .
From the basic concepts of progressions we know that the formula for finding the ${{n}^{th}}$ term of any given sequence is given as ${{T}_{n}}=a+\left( n-1 \right)d$ where $a$ is the first term and $d$ is the common difference of the sequence.
By applying this formula we will have $\Rightarrow {{T}_{n}}=4+\left( n-1 \right)4$ since 4 is the first term and common difference in the given sequence.
Therefore we can conclude that the ${{n}^{th}}$ of the given sequence $4,8,12,16,...$ will be given as $4n$.

Note: While answering questions of this type we should be sure with the concepts that we are going to apply and the calculations that we are going to perform in between the steps of the process. Similar to the arithmetic progression we have geometric progression where succeeding terms have a common ratio and its ${{n}^{th}}$ term is given as $a{{r}^{n-1}}$.