Question

Find the common difference and write the next four terms of each of the following arithmetic progressions:
(i)1,-2,-5,-8,..
(ii)0,-3,-6,-9,...
(iii)-1,1/4,3/2,...
(iv)-1,-5/6,-2/3,...

Answer 1

Find the Common difference and write next four terms.

• A Sequence in a arithmetic progression is

a- 2d, a- d, a, a+d, a+2d and so on where d is the difference.

(i) 1,-2,-5,-8

•Here the difference is -3. So the next terms in the sequence are as follows 1,-2,-5,-8,-11,-14,-17,-20...

(ii) 0,-3,-6,-9

•Here the difference is -3. So the next terms in the sequence are as follows

0,-3,-6,-9,-12,-15,-18,-21...

(iii) -1,1/4,3/2

•Here the difference is 5/4. So the next terms in the sequence are as follows

-1, 1/4, 3/2, 11/4, 4, 21/4, 13/2..

(iv) -1,-5/6,-2/3

•Here the difference is 1/6. So the next terms in the sequence are as follows

-1, -5/6, -2/3 , -1/2, -1/3 , -1/6 , 0...

Answer 2

(i)

Common difference = -3

The arithmetic progression is

1,-2,-5,-8,-11,-14,-17,-20,.......

(ii)

Common difference = -3

The arithmetic progression is

0,-3,-6,-9,-12,-15,-18,-21,.......

(iii)

Common difference $=\frac{5}{4}$

The arithmetic progression is

$-1, \frac{1}{4},\frac{3}{2},\frac{11}{4},4, \frac{21}{4},\frac{13}{2}$ .........

(iv)

Common difference $=\frac{1}{6}$

The arithmetic progression is

$-1,-\frac{5}{6},-\frac{2}{3}, -\frac{1}{2}, -\frac{1}{3},-\frac{1}{6},0$,............

Step-by-step explanation:

Arithmetic progression: A arithmetic progression is also known as arithmetic sequence.The difference between any two consecutive terms is also same.

The first term of the sequence = a

Common difference = d

(i)

Given sequence is

1,-2,-5,-8,......

Common difference = Second term - first term

                                  = -2-1

                                  = -3

The next 4 terms of the arithmetic progression are

{-8+(-3)}= -11, {-11+(-3)}=-14, {-14+(-3)}=-17, {-17+(-3)}= -20

(ii)

Given sequence is

0,-3,-6,-9,......

Common difference = Second term - first term

                                  = -3-0

                                  = -3

The next 4 terms of the arithmetic progression are

{-9+(-3)}= -12, {-12+(-3)}=-15, {-15+(-3)}=-18, {-18+(-3)}= -21

(iii)

Given sequence is

-1,$\frac{1}{4}$ , $\frac{3}{2}$,........

Common difference = Second term - first term

                                 $=\frac{1}{4}-(-1)$

                                $=\frac{5}{4}$

The next 4 terms of the arithmetic progression are

$(\frac{3}{2}+\frac{5}{4})=\frac{11}{4}$, $(\frac{11}{4}+\frac{5}{4})=\frac{16}{4}=4$, $(\frac{16}{4}+\frac{5}{4})=\frac{21}{4}$,$(\frac{21}{4}+\frac{5}{4})=\frac{26}{4}=\frac{13}{2}$

(iv)

Given sequence is

-1,$-\frac{5}{6}$ , $-\frac{2}{3}$,........

Common difference = Second term - first term

                                 $=-\frac{5}{6}-(-1)$

                                $=\frac{1}{6}$

The next 4 terms of the arithmetic progression are

$(-\frac{2}{3}+\frac{1}{6})=-\frac{3}{6}=-\frac{1}{2}$, $(-\frac{3}{6}+\frac{1}{6})=-\frac{2}{6}=-\frac{1}{3}$,$(-\frac{2}{6}+\frac{1}{6})=-\frac{1}{6}$,$-\frac{1}{6}+\frac{1}{6}=0$