Question

Consider the A.P 4, 11, 18 25, 32, ...... The term ${{t}_{n}}$ in this A.P is 368. Find n.

Answer 1

Hint: Here we have given an arithmetic progression which is a sequence of numbers in such a way that the difference of two successive numbers are constant. So, we will first find out the value of the first term and the common difference of the given arithmetic progression. Then we will use the formula of ${{t}_{n}}$ to get the value of n.

Complete step by step solution:

Now, we will find the value of “n” in the arithmetic progression by the formula as given below;
${{\text{t}}_{n}}\text{=}a+(n-1)d$ where “a” is the first term , n is the number at this position in arithmetic progression and “d” is common difference of the arithmetic progression.
So, for the given arithmetic progression we have a=4 , d= (11- 4) = 7 and ${{t}_{n}}$= 368.
\[\begin{align}
  & \Rightarrow 368=4+(n-1)7 \\
 & \Rightarrow 368-4=(n-1)7 \\
 & \Rightarrow \dfrac{364}{7}=n-1 \\
 & \Rightarrow n=52+1=53 \\
\end{align}\]
Therefore we get the value of n is equal to 53 for the above given arithmetic progression.

Note: Just remember the formula of the arithmetic progression for the ${{t}_{n}}$ term very clearly and also go through the other formulae of arithmetic progression as it will be very helpful in these types of questions.
Also be careful while doing calculation because there is a chance that you might make mistakes during calculation.