Question

Which term of the sequence -1, 3, 7, 11,…… is 95?

Answer 1

Hint: In Order to solve this problem we need to consider this series and check what it is, then we have to find the rest of the things then put the value of $n^{th}$ term as 95 then find the value of n using the general formula as per the series. Doing this will solve your problem.

Complete step by step answer:
The given series is -1, 3, 7, 11,……
Let’s check if the series is an AP.
So, second term – first term = 3 - (- 1) = 4
Third term – second term = 7 - 3 = 4
Similarly we see between the other terms that the common difference is 4 so, this series is an AP.
This series is an AP
Here we can clearly see that -1 is first term = a.
The common difference is 3-(-1) = 4 = d
Here we need to find which term is 95.
So we will use the formula ${a_n} = a + (n - 1)d$ and assume that nth term is 95.
Therefore, ${a_n}$ = 95 then on putting the value in the formula ${a_n} = a + (n - 1)d$ we get,
$ \Rightarrow 95 = - 1 + (n - 1)4$
On solving further we get,
$ \Rightarrow $4(n – 1) = 95+1
$ \Rightarrow $4(n-1) =96
$ \Rightarrow $ n-1 = 24
Therefore, n =25
Hence ${25^{th}}$ term is 95 of the series -1, 3, 7, 11, ……

So, the right answer is 24.

Note: When you get such problems you need to consider the series as AP, GP or HP and then solve accordingly to get the asked term HP is a series whose inverse is in AP this information will get all the terms related to HP whereas GP deals with the ratios involved in the series. In this problem you need to know that an arithmetic progression is a sequence of numbers such that the difference of any two successive members is a constant. For example, the sequence 1, 2, 3, 4,... is an arithmetic progression with common difference 1. Knowing this will solve all such problems.