Question

for the following APs write the first term and the common difference​

Answer 1

(i) 3, 1, - 1, - 3 …

Here, first term, a = 3

Common difference, d = Second term - First term

= 1 - 3 = - 2

(ii) - 5, - 1, 3, 7 …

Here, first term, a = - 5

Common difference, d = Second term - First term

= ( - 1) - ( - 5) = - 1 + 5 = 4

(iii) 1/3, 5/3, 9/3, 13/3 ....

Here, first term, a = 1/3

Common difference, d = Second term - First term  

= 5/3 - 1/3 = 4/3

(iv) 0.6, 1.7, 2.8, 3.9 …

Here, first term, a = 0.6

Common difference, d = Second term - First term

= 1.7 - 0.6

= 1.1

Answer 2

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FORMULA TO BE IMPLEMENTED

If

$a, a+d, a + 2d, a+3d, a+ 4d,............$

is an Arithmetic Progression

Then First Term = a

Second Term = a + d

Common Difference

= Second Term - First Term = (a + d) - a = d

CALCULATION

I.

The give Arithmetic Progression is

3, 1, - 1, - 3,........

Then First Term = 3

Second Term = 1

Common Difference

= Second Term - First Term = 1 - 3 = - 2

II.

The give Arithmetic Progression is

-5 , - 1, 3 , 7 ,........

Then First Term = - 5

Second Term = - 1

Common Difference

= Second Term - First Term

= - 1-(-5) = - 1 + 5 = 4

III.

The give Arithmetic Progression is

$\frac{1}{3} , \frac{5}{3} , \frac{9}{3} , \frac{13}{3} ,........$

Then First Term = $\frac{1}{3}$

Second Term = $\frac{5}{3}$

Common Difference

= Second Term - First Term = $\frac{5}{3} - \frac{1}{3} = \frac{4}{3}$

IV

The give Arithmetic Progression is

0.6 , 1.7 , 2.8 , 3.9 ,........

Then First Term = 0.6

Second Term = 1.7

Common Difference

= Second Term - First Term = 1.7 - 0.6 = 1.1