Question

Find the common difference and write the next four terms of each of the following arithmetic progression: $0.-3,-6,-9,......$

Answer 1

Ans.

given A.P is

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

hence the common difference is given by $d=a_{n+1}-a_n$

by putting n=1 in above equation

$d=a_2-a_1=(-3)-\left(0\right)$

$d=-3$

first term of this A.P is

$a_1=0$

the nth term of this A.P is given by

$a_n=a_1+(n-1)d$

$⟹a_n=0+(n-1)(-3)$

$⟹a_n=-3n+3$

$⟹a_n=3-3n\dots .eq\left(1\right)$

finding next four terms of A.P

1) for finding the 5th term of sequence $\left(a_5\right)$ put n=5 in eq(1)

$⟹a_5=3-3\times 5$

$⟹a_5=3-15$

$⟹a_5=-12$

2) for finding the 6th term of sequence $\left(a_6\right)$put n=6 in eq(1)

$⟹a_6=3-3\times 6$

$⟹a_6=3-18$

$⟹a_6=-15$

3) for finding the 7th term of sequence $\left(a_7\right)$put n=7 in eq(1)

$⟹a_7=3-3\times 7$

$⟹a_7=3-21$

$⟹a_7=-18$

4) for finding the 8th term of sequence $\left(a_8\right)$put n=8 in eq(1)

$⟹a_8=4-3\times 8$

$⟹a_8=3-24$

$⟹a_8=-21$