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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