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.