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Arithmetic Progressions — Maths STD 10 — Question

Maharashtra BoardEnglish MediumSTD 10MathsArithmetic Progressions2 Marks
Question
Find:Which term in the A.P. $21, 42, 63, 84$, ..... is $420$?
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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, $a_n=a+(n-1) d$.
A.P. $21,42,63,84, \ldots . . .420$
Here first term (a) $=21$
Common difference $( d )=42-21=21$
Now $a_n=a+(n-1) d$
$\Rightarrow 420=21+(n-1) \times 21$
$\Rightarrow 420=21+21 n-21 \Rightarrow 420=21 n$
$\Rightarrow n=\frac{420}{21}=20$
$\therefore 420$ is the $20^{\text {th }}$ term.

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