Question

Which term of the AP –1, 3, 7,..... is 95?

Answer 1

Hint: Here we may apply the formula used to find a general term or nth term of any AP. Since, here the value of the term is known, using this formula will give us the value of n that is the place at which that term is present in the AP.

Complete step-by-step answer:

Let us find the common difference of this AP. Since, we know that the common difference of an AP is the difference of a term and its successive term of the AP and this common difference is always constant for an AP.
So, for the given AP:
Common difference (d) = 3 – (-1) = 4
Also when we subtract the 2nd term from the 3rd term, we get:
d=7-3=4
So, we can see that the common difference is 4 which is a constant.
The formula used for a general term of an AP is given as:
${{a}_{n}}=a+\left( n-1 \right)d............\left( 1 \right)$
Here a and d are the first term and common difference respectively of this given AP.
So, on substituting the values we have in equation (1), we get:
${{a}_{n}}=-1+\left( n-1 \right)4$
Since, here ${{a}_{n}}$ represents the value of the nth term which is 95 in this case. So, using this we have to find the value of n. On substituting this value we get:
$\begin{align}
  & 95=-1+\left( n-1 \right)4 \\
 & 95=-1+4n-4 \\
 & 95=-5+4n \\
 & 100=4n \\
 & n=\dfrac{100}{4} \\
 & n=25 \\
\end{align}$

So, the value of n is 25.
Hence, 95 occurs at the 25th place in the given AP.

Note: Students should note here that the common difference of an AP is constant. So, we can take the difference of any two consecutive terms to find the AP but there will be a mistake if the difference is taken for non consecutive terms.