CBSE BoardEnglish MediumSTD 10MathsArithmetic Progressions2 Marks
Question
Write the $n^{th}$ ter, of the A.P. $\frac{1}{\text{m}},\frac{1+\text{m}}{\text{m}},\frac{1+2\text{m}}{\text{m}}, .....$
✓
Answer
Given: A.P. $\frac{1}{m}, \frac{1+ m }{ m }, \frac{1+2 m}{ m }, \ldots$.
We know that the $n^{\text {th }}$ term of an A.P. is given by
$a_n=a+(n-1) d$
In the given A.P..
$\text{a}=\frac{1}{\text{m}}$
$\text{d}=\frac{1+\text{m}}{\text{m}}-\frac{1}{\text{m}}=\frac{1+\text{m}-1}{\text{m}}=1$
Thus, the $n ^{\text {th }}$ term of the given A.P. is
$\text{a}_\text{n}=\frac{1}{\text{m}}+(\text{n}-1)1=\frac{1+(\text{n}-1)\text{m}}{\text{m}}$
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