Question

Hello; I need help on an assignment about arithmetic sequences and series. I will re-write one of the word problems. There are 130 students in grade one, 210 students in grade two and 290 students in grade three in a primary school... and so on in an arithmetic sequence. What is the total amount of students in the primary school? (6 grade levels)

Answer 1

Given:

130, 210, 290,...

total of 6 grade levels

Asked: What is the total amount of students in primary school?

Solution:

To find the total amount of students, we will need the formula to the sum of all terms in arithmetic progression.

Formula of Sum of all terms in Arithmetic Progression:

$S=\frac{n}{2}\lbrack2a+(n-1)d\rbrack$

where:

S = sum of all terms

n = total grade levels

a = first term

d = common difference

Now, we will first find the common difference.

d = 210 - 130

d = 80

a = 130

n = 6

Let's substitute the acquired data to the formula.

$\begin{gathered} S=\frac{n}{2}\lbrack2a+(n-1)d\rbrack \\ S=\frac{6}{2}\lbrack2\cdot130+(6-1)80\rbrack \\ S=\frac{6}{2}\lbrack260+400\rbrack \\ S=3\cdot660 \\ S=1980 \end{gathered}$

ANSWER: 1980 total students