Question
Find:
Which term in the A.P. $4,9,14, \ldots .$. is $254 ?$
Which term in the A.P. $4,9,14, \ldots .$. 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 $n ^{\text {th }}$ 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 $254.$
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 $n ^{\text {th }}$ 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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