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

3+8+13+18+…



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User Robotronx
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2 Answers

21 votes
21 votes

Answer:

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

User Kine
by
3.1k points
14 votes
14 votes

Answer:

  • 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

User Egg Vans
by
2.8k points