Enter Sequence Function

Enter # of terms


Answer
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S15 = 240

↓Steps Explained:↓

Final Answer

S15 = 240

And the Sum of the first 15 terms for:

2,4,6,8,10

Explicit Formula

an = a1 + (n - 1)d

Define d

d = Δ between consecutive terms

d = an - an - 1

We see a common difference = 2

We have a1 = 2

an = 2 + 2(n - 1)

Calculate Term (6)

Plug in n = 6 and d = 2

a6 = 2 + 2(6 - 1)

a6 = 12

a6 = 2 + 2(5)

a6 = 2 + 10

Calculate Term (7)

Plug in n = 7 and d = 2

a7 = 2 + 2(7 - 1)

a7 = 14

a7 = 2 + 2(6)

a7 = 2 + 12

Calculate Term (8)

Plug in n = 8 and d = 2

a8 = 2 + 2(8 - 1)

a8 = 16

a8 = 2 + 2(7)

a8 = 2 + 14

Calculate Term (9)

Plug in n = 9 and d = 2

a9 = 2 + 2(9 - 1)

a9 = 18

a9 = 2 + 2(8)

a9 = 2 + 16

Calculate Term (10)

Plug in n = 10 and d = 2

a10 = 2 + 2(10 - 1)

a10 = 20

a10 = 2 + 2(9)

a10 = 2 + 18

Calculate Term (11)

Plug in n = 11 and d = 2

a11 = 2 + 2(11 - 1)

a11 = 22

a11 = 2 + 2(10)

a11 = 2 + 20

Calculate Term (12)

Plug in n = 12 and d = 2

a12 = 2 + 2(12 - 1)

a12 = 24

a12 = 2 + 2(11)

a12 = 2 + 22

Calculate Term (13)

Plug in n = 13 and d = 2

a13 = 2 + 2(13 - 1)

a13 = 26

a13 = 2 + 2(12)

a13 = 2 + 24

Calculate Term (14)

Plug in n = 14 and d = 2

a14 = 2 + 2(14 - 1)

a14 = 28

a14 = 2 + 2(13)

a14 = 2 + 26

Calculate Term (15)

Plug in n = 15 and d = 2

a15 = 2 + 2(15 - 1)

a15 = 30

a15 = 2 + 2(14)

a15 = 2 + 28

Calculate Sn:

Sn  =  n(a1 + an)
  2

Substituting n = 15, we get:

S15  =  15(a1 + a15)
  2

S15  =  15(2 + 30)
  2

S15  =  15(32)
  2

S15  =  480
  2


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