Answer:
[tex]f(n)=\frac{n(n+1)}{2}[/tex]
Step-by-step explanation:
We are given that a sequence
1,3,6,10,15,21,28
We have to write a sequence as a function.
[tex]a_1=1[/tex]
[tex]a_2=3[/tex]
[tex]a_3=6[/tex]
[tex]a_4=10[/tex]
[tex]a_5=15[/tex]
[tex]a_6=21[/tex]
[tex]a_7=28[/tex]
[tex]a_1=1[/tex]
[tex]a_2=1+2=3[/tex]
[tex]a_3=1+2+3=6[/tex]
:
:
:
[tex]a_7=1+2+3+4+5+6+7=28[/tex]
Therefore, [tex]a_n=\sum_{n=1}^{n=k}n[/tex]
[tex]f(n)=\frac{n(n+1)}{2}[/tex]
Because [tex]\sum n=\frac{n(n+1)}{2}[/tex]
Therefore, the given sequence can be written as function
[tex]f(n)=\frac{n(n+1)}{2}[/tex]
