Find the first term and common difference for each of the A.P. 1 … - Vidyadip

Question

Find the first term and common difference for each of the A.P.
$\frac{1}{4}, \frac{3}{4}, \frac{5}{4}, \frac{7}{4}, \ldots$

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Answer

$\frac{1}{4}, \frac{3}{4}, \frac{5}{4}, \frac{7}{4}, \ldots$
First term $a _1=\frac{1}{4}$
Second term $a _2=\frac{3}{4}$
Third term $a _3=\frac{5}{4}$
We know that $d=a_{n+1}-a_n$
Thus, $d = a _2- a _1=\frac{3}{4}-\frac{1}{4}=\frac{2}{4}=\frac{1}{2}$
Hence, the common difference $d =\frac{1}{2}$ and first term is $\frac{1}{4}$

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