Answer:
1,890
Step-by-step explanation:
It's an arithmetic sequence. Why? Because the different is constant.
[tex]a_n=4n+1\\\\a_{n+1}=4(n+1)+1=4n+4+1=4n+5\\\\a_{n+1}-a_n=(4n+5)-(4n+1)=4n+5-4n-1=4=const.[/tex]
The formula of a sum of an arithmetic sequence:
[tex]S_n=\dfrac{2a_1+(n-1)d}{2}\cdot n[/tex]
We have d = 4 and n = 30. Calculate a₁. Put n= 1 to the expression:
[tex]a_1=4(1)+1=4+1=5[/tex]
Substitute:
[tex]S_{30}=\dfrac{2(5)+(30-1)(4)}{2}\cdot30=(10+(29)(4))(15)=(10+76)(15)\\\\=(126)(15)=1,890[/tex]
