Question
Which term of the sequence $3, 8, 13, ........$ is $78$?
✓
Answer
The given sequence is $3, 8, 13, …..$
Now,
$8 - 3 = 13 - 8 = 5$
Hence, the given sequence is an A.P. with first term $a = 3$ and common difference $d = 5.$
Let the $n^{th}$ term of the given A.P. be 78.
$\Rightarrow 78 = 3 + (n - 1)(5)$
$\Rightarrow 75 = 5n - 5$
$\Rightarrow 5n = 80$
$\Rightarrow n = 16$
Thus, the $16^{th}$ term of the given sequence is $78$.
Now,
$8 - 3 = 13 - 8 = 5$
Hence, the given sequence is an A.P. with first term $a = 3$ and common difference $d = 5.$
Let the $n^{th}$ term of the given A.P. be 78.
$\Rightarrow 78 = 3 + (n - 1)(5)$
$\Rightarrow 75 = 5n - 5$
$\Rightarrow 5n = 80$
$\Rightarrow n = 16$
Thus, the $16^{th}$ term of the given sequence is $78$.
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