Question

Write each sequence as a function.
a. {1, 3, 6, 10, 15, 21, 28}

Answer 1

`f(n)=(n(n+1))/(2)`

Explanation:

We are given that a sequence

1,3,6,10,15,21,28

We have to write a sequence as a function.

`a_1=1`

`a_2=3`

`a_3=6`

`a_4=10`

`a_5=15`

`a_6=21`

`a_7=28`

`a_1=1`

`a_2=1+2=3`

`a_3=1+2+3=6`

:

:

:

`a_7=1+2+3+4+5+6+7=28`

Therefore,
`a_n=\sum_(n=1)^(n=k)n`

`f(n)=(n(n+1))/(2)`

Because
`\sum n=(n(n+1))/(2)`

Therefore, the given sequence can be written as function

`f(n)=(n(n+1))/(2)`