Question

Suppose y = 48 + 3(2n - 1) is an explicit representation of an arithmetic sequence for integer values n ≥ 1. Find the xth partial sum of the series, as a quadratic function, where x represents the term number.

Answer 1

`a_n=48+3(2n-1)`

The formula of the sum of the arithmetic sequence:

`S_n=(a_1+a__n)/(2)\cdot n`
calculate:

`a_1=48+3(2\cdot1-1)=48+3=51`
substitute

`S_n=(51+48+3(2n-1))/(2)\cdot n=(99+6n-3)/(2)\cdot n=(96+6n)/(2)\cdot n=3n^2+48n`
Your answer is:

`\boxed{f(x)=3x^2+48x}`

Answer 2

Answer: 3x2 + 51x

Explanation: