Question
Find:
Which term of the $A.P. 3, 8, 13, .....$ is $248?$
Which term of the $A.P. 3, 8, 13, .....$ is $248?$
✓
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, $a_n= a + (n - 1)d.$
Here,
$A.P.$ is $3, 8, 13, .....$
$a_n= 248$
$a = 3$
Now,
Common difference $(d) = a_1- a$
$= 8 - 3$
$= 5$
Thus, using the above mentioned formula
$a_n= a + (n - 1)d$
$248 = 3 + (n - 1)5$
$248 - 3 = 5n - 5$
$245 + 5 = 5n$
$\text{n}=\frac{250}{5}$
$n = 50$
Thus, $n = 50$
Therefore $248$ is the $50^{th}$ term of the given $A.P.$
So here we will find the value of n using the formula, $a_n= a + (n - 1)d.$
Here,
$A.P.$ is $3, 8, 13, .....$
$a_n= 248$
$a = 3$
Now,
Common difference $(d) = a_1- a$
$= 8 - 3$
$= 5$
Thus, using the above mentioned formula
$a_n= a + (n - 1)d$
$248 = 3 + (n - 1)5$
$248 - 3 = 5n - 5$
$245 + 5 = 5n$
$\text{n}=\frac{250}{5}$
$n = 50$
Thus, $n = 50$
Therefore $248$ is the $50^{th}$ term of the given $A.P.$
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