For the following APs, write the first term and the common difference:
,b>(i) $3, 1, -1, -3, ……$
(ii) $-5, -1, 3, 7, ……$
(iii) $\frac{1}{3}, \frac{5}{3}, \frac{9}{3}, \frac{13}{3}, ……..$
(iv) $0.6, 1.7, 2.8, 3.9, ……$

To do:

We have to write the first term and common difference of the given A.P in each case.

Solution:

(i) Given A.P. is $3,\ 1,\ −1,\ −3,......$

First term $a=3$ 

And common difference $d=a_2−a_1$

$=1−3$

$=−2$

Therefore, the first term is $3$ and the common difference is $-2$. 

(ii) $-5, -1, 3, 7, ……$

In the given A.P.,

$a_1=-5, a_2=-1, a_3=3$

Therefore,

First term $a=a_1=-5$ Common difference $d=a_2-a_1=-1-(-5)=-1+5=4$.

The first term $a$ is $-5$ and the common difference $d$ is $4$.

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

In the given A.P.,

$a_1=\frac{1}{3}, a_2=\frac{5}{3}, a_3=\frac{9}{3}$

Therefore,

First term $a=a_1=\frac{1}{3}$

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

The first term $a$ is $\frac{1}{3}$ and the common difference $d$ is $\frac{4}{3}$.

(iv) $0.6, 1.7, 2.8, 3.9, ……$

In the given A.P.,

$a_1=0.6, a_2=1.7, a_3=2.8$

Therefore,

First term $a=a_1=0.6$ Common difference $d=a_2-a_1=1.7-0.6=1.1$.

The first term $a$ is $0.6$ and the common difference $d$ is $1.1$.

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Updated on: 10-Oct-2022

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