Question
Find:
Which term in the A.P. $4, 9, 14,$ ..... is $254$?
Which term in the A.P. $4, 9, 14,$ ..... is $254$?
✓
Answer
In the given problem, we are given an A.P. and the value of one of its term. We need to find which term it is $(n).$
So here we will find the value of n using the formula, $a_n = a + (n - 1)d.$
Given A.P. $4, 9, 14,$ .....
First term $(a) = 4$
Common difference $(d) = a_1 - a$
$= 9 - 4$
$= 5$
$n^{th}$^ term $(a_n) = a + (n - 1)d$
Given $n^{th}$^ term is $254$
$4 + (n - 1)5 = 254$
$(n - 1).5 = 250$
$\text{n}-1=\frac{250}{5}=50$
$n = 50$
$\therefore$ $51^{st}$ term is $254.$
So here we will find the value of n using the formula, $a_n = a + (n - 1)d.$
Given A.P. $4, 9, 14,$ .....
First term $(a) = 4$
Common difference $(d) = a_1 - a$
$= 9 - 4$
$= 5$
$n^{th}$^ term $(a_n) = a + (n - 1)d$
Given $n^{th}$^ term is $254$
$4 + (n - 1)5 = 254$
$(n - 1).5 = 250$
$\text{n}-1=\frac{250}{5}=50$
$n = 50$
$\therefore$ $51^{st}$ term is $254.$
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