Question
For the following arithmetic progressions write the first term a and the common difference d:
$\frac{1}{5},\frac{3}{5},\frac{5}{5},\frac{7}{5}.$
$\frac{1}{5},\frac{3}{5},\frac{5}{5},\frac{7}{5}.$
✓
Answer
$\frac{1}{5},\frac{3}{5},\frac{5}{5},\frac{7}{5}.$
Here, first term of the given A.P. is $\text{(a)}=\frac{1}{5}$
Now, we will find the difference between the two terms of the given A.P.
$\text{a}_2-\text{a}_1=\frac{3}{5}-\frac{1}{5}$
$\text{a}_2-\text{a}_1=\frac{2}{5}$
Similarly,
$\text{a}_3-\text{a}_2=\frac{5}{5}-\frac{3}{5}$
$\text{a}_3-\text{a}_2=\frac{2}{5}$
Also,
$\text{a}_4-\text{a}_3=\frac{7}{5}-\frac{5}{5}$
$\text{a}_4-\text{a}_3=\frac{2}{5}$
As $\text{a}_2-\text{a}_1=\text{a}_3-\text{a}_2=\text{a}_4-\text{a}_3=\frac{2}{5}$
Therefore, the first term of the given A.P. is $\text{a}=\frac{1}{5}$ and the common differece is $\text{d}=\frac{2}{5}$.
Here, first term of the given A.P. is $\text{(a)}=\frac{1}{5}$
Now, we will find the difference between the two terms of the given A.P.
$\text{a}_2-\text{a}_1=\frac{3}{5}-\frac{1}{5}$
$\text{a}_2-\text{a}_1=\frac{2}{5}$
Similarly,
$\text{a}_3-\text{a}_2=\frac{5}{5}-\frac{3}{5}$
$\text{a}_3-\text{a}_2=\frac{2}{5}$
Also,
$\text{a}_4-\text{a}_3=\frac{7}{5}-\frac{5}{5}$
$\text{a}_4-\text{a}_3=\frac{2}{5}$
As $\text{a}_2-\text{a}_1=\text{a}_3-\text{a}_2=\text{a}_4-\text{a}_3=\frac{2}{5}$
Therefore, the first term of the given A.P. is $\text{a}=\frac{1}{5}$ and the common differece is $\text{d}=\frac{2}{5}$.
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