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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