Question

For the following APs, find the first term and the common difference
(1) 3, 1, -1, -3 …
(2) -5, -1, 3, 7 …
(3) $\dfrac{1}{3}, \dfrac{5}{3}, \dfrac{9}{3}, \dfrac{{13}}{3}...$
(4) 0.6, 1.7, 2.8, 3.9 …

Answer 1

We will identify the first term. The common difference of an AP is the difference between any two consecutive terms of the AP. Then, we will Subtract $1^{st}$ term from the $2^{nd}$ term and hence the common difference.

Complete step by step solution:
We can see that; the first term of the given AP is $a = 3$
The Common difference of the given AP is $d = 1 - 3 \Rightarrow d = - 2$
(2) We can see that; the first term of the given AP is $a = - 5$
The Common difference of the given AP is $d = - 1 - ( - 5) \Rightarrow d = - 1 + 5 \Rightarrow d = 4$
(3) We can see that; the first term of the given AP is $a = \dfrac{1}{3}$
The Common difference of the given AP is $d = \dfrac{5}{3} - \dfrac{1}{3} \Rightarrow d = \dfrac{4}{3}$
(4) We can see that; the first term of the given AP is $a = 0.6$
The Common difference of the given AP is $d = 1.7 - 0.6 \Rightarrow d = 1.1$

Note:
It is important to know that the common difference is equal throughout the AP. The AP whose common difference is positive, is an increasing sequence as each term of such sequence is greater than its previous term. Similarly, the AP whose common difference is negative, is a decreasing sequence as each term of such sequence is lesser than its previous term. Observe that, in (1) the AP is a decreasing sequence while for (2), (3) & (4) they are increasing sequences.