Find the sum of the arithmetic series.

Question

Find the sum of the arithmetic series.

Answer 1

To find the first term, use i = 1 for 2i and you get 2(1) = 2

To find the 2nd term, use i = 2 for 2i and you get 2(2) = 4

To find the 3rd term, use i = 3 for 2i and you get 2(3) = 6

To find the 4th term, use i = 4 for 2i and you get 2(4) = 8

To find the 5th term, use i = 5 for 2i and you get 2(5) = 10

To find the 6th term, use i = 6 for 2i and you get 2(6) = 12

To find the 7th term, use i = 7 for 2i and you get 2(7) = 14

To find the 8th term, use i = 8 for 2i and you get 2(8) = 16

To find the 9th term, use i = 9 for 2i and you get 2(9) = 18

To find the 10th term, use i = 10 (the last value of i) for 2i and you get 2(10) = 20

So the sum of these is 2 + 4 + 6 + 8 + 10 + 12 + 14 + 16 + 18 + 20 = ?

You can also use the equation:

we are looking for S₁₀ and we know n = 10, a₁ = 2, a₁₀ = 20 so S₁₀ = (10)(2 + 20)/2= ?

Answer 2

S₁₀ = (10/2)[2(2) + 9(2)] Standard formula, Learn it.