Question

The sequence an = 5n + 3 is the same as the sequence a1 = 8, an = an-1 + 5.

TRUE or FALSE
**Please explain! :) Thanks! :)

Answer 1

Both sequence are same, so the given statement is true.

Explanation:

The first sequence is defined as

`a_n=5n+3` ..... (1)

The second sequence is defined as

`a_1=8`

`a_n=a_(n-1)+5`

It can be written as

`a_n-a_(n-1)=5`

The common difference of the sequence is

`d=a_n-a_(n-1)=5`

The first term of the sequence is 8 and common difference is 5.

The second sequence can defined as

`a_n=a+(n-1)d`

`a_n=8+(n-1)5`

`a_n=8+5n-5`

`a_n=5n+3` .....(2)

From (1) and (2), we can say that both sequence are same.

Therefore the given statement is true.