Question
Find:
Is $302$ a term of the A.P. $3, 8, 13, .....?$
Is $302$ a term of the A.P. $3, 8, 13, .....?$
✓
Answer
In the given problem, we are given an A.P. and the Value of one of its term.
We need to find whether it is a term of the A.P. or not so here we will use the formula $a_n = a + (n - 1)d.$
Here,
A.P.$ = 3, 8, 13, .....$
First term $(a) = 3$
and Common difference $(d) = 8 - 3 = 5$
Let $a_n = 302$, then
$302 = a + (n - 1)d = 3 + (n - 1) \times 5$
$\Rightarrow 302 = 3 + 5n - 5$
$\Rightarrow 302 - 3 + 5 = 5n$
$\Rightarrow\ 304=5\text{n}\Rightarrow\text{n}=\frac{304}{5}=60\frac{4}{5}$
Since n is not a natural number
$\therefore$ $302$ is not a term of the given sequence.
We need to find whether it is a term of the A.P. or not so here we will use the formula $a_n = a + (n - 1)d.$
Here,
A.P.$ = 3, 8, 13, .....$
First term $(a) = 3$
and Common difference $(d) = 8 - 3 = 5$
Let $a_n = 302$, then
$302 = a + (n - 1)d = 3 + (n - 1) \times 5$
$\Rightarrow 302 = 3 + 5n - 5$
$\Rightarrow 302 - 3 + 5 = 5n$
$\Rightarrow\ 304=5\text{n}\Rightarrow\text{n}=\frac{304}{5}=60\frac{4}{5}$
Since n is not a natural number
$\therefore$ $302$ is not a term of the given sequence.
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