Question

What is the sum of the first 19 terms of the arithmetic series?

3+8+13+18+…



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Answer 1

912

Explanation:

Sum of the first n terms of an arithmetic series:

`S_n=\frac12n[2a+(n-1)d]`

where:

• n = nth term
• a = first term
• d = common difference

Given arithmetic series: 3 + 8 + 13 + 18 + ...

Therefore:

• a = 3
• d = 8 - 3 = 5

To find the sum of the first 19 terms, substitute the given values together with n = 19 into the Sum formula:

`\implies S_(19)=(1)/(2)(19)\left[\:2(3)+5(19-1)\:\right]`

`\implies S_(19)=(19)/(2)\left[\:6+90\:\right]`

`\implies S_(19)=(19)/(2)\left[\:96\:\right]`

`\implies S_(19)=912`

Answer 2

• 912

Explanation:

Given the AP

• 3, 8, 13, 18, ...

We can see that

• The first term is a = 3
• The common difference is d = 5

The sum of the first n terms formula is

`S_n=\cfrac{n}{2} [2a+(n-1)d]`

Substitute the values and considering n = 19, find the sum

`S_(19)=\cfrac{19}{2} [2*3+(19-1)*5]=\cfrac{19}{2} [6+90]=912`