Question

Find the sum of the first 30 terms of the sequence below an=4n+1

Answer 1

1,890

Explanation:

It's an arithmetic sequence. Why? Because the different is constant.

`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.`

The formula of a sum of an arithmetic sequence:

`S_n=(2a_1+(n-1)d)/(2)\cdot n`

We have d = 4 and n = 30. Calculate a₁. Put n= 1 to the expression:

`a_1=4(1)+1=4+1=5`

Substitute:

`S_(30)=(2(5)+(30-1)(4))/(2)\cdot30=(10+(29)(4))(15)=(10+76)(15)\\\\=(126)(15)=1,890`