Question

A sequence (an) is given by formula An =10 -3n show that sequence is an AP

Answer 1

a(n-1) = 10- 3(n-1) = 10-3n+3
= 13 -3n

an - a(n-1) = 10 -3n -10+3n -3
= -3

SO it's an AP with common difference -3

Answer 2

An = 10 - 3n

Putting value of n,

Let n = 1 ,

Then,

A1 = 10 - 3 *1

A1 = 7

For n = 2,

A2 = 10 - 3 *2

A2 = 10 - 6 = 4

For n = 3 ,

A3 = 10 - 3 * 3

A3 = 10 - 9 = 1

Now,

A2 - A1 = 4 - 7 = - 3 = d

A3 - A2 = 1 - 4 = - 3 = d

Since, Difference is common.

So, Common difference is same.

Hence, The given sequence is in A. P.