Question

Find the $nth$ term of the A.P. $13,8,3, - 2,..............$

Answer 1

Hint: If a series of $n$ terms is in Arithmetic Progression (A.P) with first term $a$, common difference $d$ then the $nth$ term of the series is given by ${T_n} = a + \left( {n - 1} \right)d$. So, use this concept to reach the solution of the given problem.

Complete step-by-step answer:

Given series are $13,8,3, - 2,..............$

We know that if a series of $n$ terms is in Arithmetic Progression (A.P) with first term $a$, common difference $d$ then the $nth$ term of the series is given by ${T_n} = a + \left( {n - 1} \right)d$.

In the given series $a = 13$
Common difference ($d$) = second term – first term
= 8 – 13
= -5
Therefore, ${T_n} = a + \left( {n - 1} \right)d$

Substituting $a = 13{\text{ }}\& {\text{ }}d = - 5$ we have,

$$\Rightarrow {T_n} = 13 + \left( {n - 1} \right)\left( { - 5} \right) \\\ \Rightarrow {T_n} = 13 - 5n + 5 \\\ \therefore {T_n} = 18 - 5n \\\$$

Thus, the $nth$ term of the A.P. $13,8,3, - 2,..............$ is $18 - 5n$.

Note: The arithmetic mean is the simplest and most widely used measure of a mean, or average. It simply involves taking the sum of a group of numbers, then dividing that sum by the count of the numbers used in the series.