Question

NO LINKS!!!

Find the sum of the finite arithmetic sequence.
Sum of the first 150 positive integers

Answer 1

11325

Explanation:

`\boxed{\begin{minipage}{7.3 cm}\underline{Sum of the first $n$ terms of an arithmetic series}\\\\$S_n=(1)/(2)n[a+l]$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the first term. \\ \phantom{ww}$\bullet$ $l$ is the last term.\\\phantom{ww}$\bullet$ $n$ is the number of terms.\\\end{minipage}}`

A positive integer is a whole number that is greater than zero.

Therefore:

• The first term, a, of the first 150 positive integers is 1.
• The last term, l, of the first 150 positive integers is 150.
• The number of terms, n, is 150.

Substitute the values into the formula to find the sum of the first 150 positive integers:

`\implies S_(150)=(1)/(2)(150)\left[1+150\right]`

`\implies S_(150)=75 \cdot 151`

`\implies S_(150)=11325`