Question

In an $A.P$ if $a = 12,d = 4,{T_n} = 76$, find $n$

Answer 1

Hint: In this question, we have to find out the value of $n$. $n$ means the number of terms. As it is in arithmetic progression terms given are of their respective meaning. Using the relation, $l = a + (n - 1)d$, we can work out the value of $n$, by putting the value given. In the relation $'l'$ is the last term of $AP$ series, $d$ is difference and $a$ is the first term.

Complete step-by-step answer:
In arithmetic progression –
Let, first term of an $A.P$ be $'a'$
And, given that $a = 12$
Again, difference between terms are $'d'$
& given that $d = 4$
Last term of an $A.P$$ = L$
& $l = 76$ (given)
Consider number of terms $ = n$
According to $A.P$ -
$l = a + (n - 1)d$
Putting individuals’ value, we get
$
  76 = 12 + (n - 1) \times 4 \\
   \Rightarrow 64 = (n - 1) \times 4 \\
   \Rightarrow (n - 1) = 16 \\
   \Rightarrow n = 17 \\
$
Therefore, number of terms asked is $17$

Note: The above question was asked from the topic of Arithmetic progression so we need to have a concept of it very clear in our mind that will help us to strike the way it should be done. There is a chapter called series & sequences, and a conceptual topic $A.P,G.P$& $H.P$are parts of it. Calculations should be done very carefully to avoid silly mistake instead of knowing the concepts & procedures to be applied .As this problem is based on A.P , so we should also know what it is .$A.P$is a series which proceeding one by a constant quantity (e.g. $1,2,3,4$etc. $9,7,5,3$).