Courses
Courses for Kids
Free study material
Offline Centres
More
Store Icon
Store

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 …

seo-qna
Last updated date: 15th Jun 2024
Total views: 402.3k
Views today: 5.02k
Answer
VerifiedVerified
402.3k+ views
Hint:
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.