Which term of A.P 3, 10, 17, .... Will be 84 more than its 13^ th… - Vidyadip

Question

Which term of A.P $3, 10, 17, ....$ Will be $84$ more than its $13^{th}$ term?

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Answer

The given A.P is $3, 10, 17, ....$
Here $a = 3,$ and $d = 10 - 3 = 7$
Now
$t_{13}=a+12 d=3+12 \times 7=3+84=87$
Let the required term be nth term
$\therefore t_n-t_{13}=84$
$\Rightarrow [a + (n - 1)d] - 87 = 84$
$\Rightarrow 3+(n-1) \times 7=171$
$\Rightarrow(n-1) \times 7=168$
$\Rightarrow n -1=24$
$\Rightarrow n =25$
Thus required term $= 25^{th}$ term

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