Write each sequence as a function.a. {1, 3, 6, 10, 15, 21, 28}
Accepted Solution
A:
Answer:[tex]f(n)=\frac{n(n+1)}{2}[/tex]Step-by-step explanation: We are given that a sequence 1,3,6,10,15,21,28We 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]