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Arithmetic Progressions — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsArithmetic Progressions3 Marks
Question
Is $68$ a them of the A.P. $7, 10, 13, ...?$
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Answer

Is $168$ a term of A.P. $7, 10, 13, ...?$
Here, $\text{a}=7$
and $\text{x}=10-7=3$
$\therefore\text{a}_\text{n}$ term is $=\text{a}+(\text{n}-1)\text{d}$
Let $68$ be $n^{th}$​​​​​​​ temr of A.P.
Then,
$68=7+3(\text{n}-1)$
$\Rightarrow68=7+3\text{n}-3$
$\Rightarrow68-4=3\text{n}$
$\Rightarrow64=3\text{n}$
$\Rightarrow\text{n}=\frac{64}{3}$
Which is note natural number.
$\therefore$ $68$ nota term of given A.P.

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