Question

Write the sequence with $n$th term. Show that all the sequences form A.P $a_n=6-n$

Answer 1

Given, the nth term of the sequence is

$a_n=6-n...................eq\left(1\right)$

1) for finding the first term of sequence $\left(a_1\right)$ put n=1 in eq(1)

$a_1=6-1$

$⟹a_1=5$

2) for finding the second term of sequence $\left(a_2\right)$put n=2 in eq(1)

$a_2=6-2$

$⟹a_2=4$

3) for finding the third term of sequence $\left(a_3\right)$ put n=3 in eq(1)

$a_3=6-3$

$⟹a_3=3$

4) for finding the fourth term of sequence $\left(a_4\right)$ put n=4 in eq(1)

$a_4=6-4$

$⟹a_4=2$

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

$a_5=6-5$

$⟹a_5=1$

.

.

and so on.

hence this sequence form an A.P with first term a=5 and commo difference d=-1

and the sequence can be written as

$5,4,3,2,1,....$