Question

For the following arithmetic progression write the first term and common difference
(i) $\frac{1}{3},\frac{5}{3},\frac{9}{3},\frac{13}{3},...$
(ii) $0.6,1.7,2.8,3.9,...$

Answer 1

(i) We have,

$\frac{5}{3}-\frac{1}{3}=\frac{4}{3},\frac{9}{3}-\frac{5}{3}=\frac{4}{3},\frac{13}{3}-\frac{9}{3}=\frac{4}{3}$

Clearly, the difference between a term and the preceding term is the same and is equal to $\frac{4}{3}$.
So, the given sequence is an A.P. with first term $\frac{1}{3}$ and common difference $\frac{4}{3}$.
(ii) We have,

$1.7-0.6=1.1,2.8-1.7=1.1,3.9-2.8=1.1$

So, the given sequence is an A.P. with first term $0.6$ and a common difference $1.1$.