For the following APs, write the first term and the common

Q) For the following APs, write the first term and the common difference:

(iii) $\frac{1}{3}, \frac{5}{3}, \frac{9}{3}, \frac{13}{3}$ ,….

Ans: Here we are given AP and we need to find the first term a and common difference d.

Now, first term of the AP, $a_1 = \frac{1}{3}$ (by observation)

Further we can see that $a_2 = \frac{5}{3}$ and $a_3 = \frac{9}{3}$

Common difference is the difference between any two consecutive terms, hence:

$d = a_2 - a_1 = \frac{5}{3} - \frac{1}{3} = \frac{4}{3}$

or $d = a_3 - a_2 = \frac{9}{3} - \frac{5}{3} = \frac{4}{3}$

Therefore, in the given AP, the first term is $\frac{1}{3}$ and common difference is $\frac{4}{3}$ .

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