Calculate the explicit formula
Calculate term number 15
And the Sum of the first 15 terms for:
2,4,6,8,10

Explicit Formula

a_n = a₁ + (n - 1)d

Define d

d = Δ between consecutive terms
d = a_n - a_{n - 1}

We see a common difference = 2
We have a₁ = 2
a_n = 2 + 2(n - 1)

Calculate Term (6)

Plug in n = 6 and d = 2
a₆ = 2 + 2(6 - 1)
a₆ = 2 + 2(6 - 1)
a₆ = 2 + 2(5)
a₆ = 2 + 10
a₆ = 12

Calculate Term (7)

Plug in n = 7 and d = 2
a₇ = 2 + 2(7 - 1)
a₇ = 2 + 2(7 - 1)
a₇ = 2 + 2(6)
a₇ = 2 + 12
a₇ = 14

Calculate Term (8)

Plug in n = 8 and d = 2
a₈ = 2 + 2(8 - 1)
a₈ = 2 + 2(8 - 1)
a₈ = 2 + 2(7)
a₈ = 2 + 14
a₈ = 16

Calculate Term (9)

Plug in n = 9 and d = 2
a₉ = 2 + 2(9 - 1)
a₉ = 2 + 2(9 - 1)
a₉ = 2 + 2(8)
a₉ = 2 + 16
a₉ = 18

Calculate Term (10)

Plug in n = 10 and d = 2
a₁₀ = 2 + 2(10 - 1)
a₁₀ = 2 + 2(10 - 1)
a₁₀ = 2 + 2(9)
a₁₀ = 2 + 18
a₁₀ = 20

Calculate Term (11)

Plug in n = 11 and d = 2
a₁₁ = 2 + 2(11 - 1)
a₁₁ = 2 + 2(11 - 1)
a₁₁ = 2 + 2(10)
a₁₁ = 2 + 20
a₁₁ = 22

Calculate Term (12)

Plug in n = 12 and d = 2
a₁₂ = 2 + 2(12 - 1)
a₁₂ = 2 + 2(12 - 1)
a₁₂ = 2 + 2(11)
a₁₂ = 2 + 22
a₁₂ = 24

Calculate Term (13)

Plug in n = 13 and d = 2
a₁₃ = 2 + 2(13 - 1)
a₁₃ = 2 + 2(13 - 1)
a₁₃ = 2 + 2(12)
a₁₃ = 2 + 24
a₁₃ = 26

Calculate Term (14)

Plug in n = 14 and d = 2
a₁₄ = 2 + 2(14 - 1)
a₁₄ = 2 + 2(14 - 1)
a₁₄ = 2 + 2(13)
a₁₄ = 2 + 26
a₁₄ = 28

Calculate Term (15)

Plug in n = 15 and d = 2
a₁₅ = 2 + 2(15 - 1)
a₁₅ = 2 + 2(15 - 1)
a₁₅ = 2 + 2(14)
a₁₅ = 2 + 28
a₁₅ = 30

Calculate S_n:

S_n = Sum of the first n terms

S_n =	n(a₁ + a_n)
	2

Substituting n = 15, we get:

S₁₅ =	15(a₁ + a₁₅)
	2

S₁₅ =	15(2 + 30)
	2

S₁₅ =	15(32)
	2

S₁₅ =	480
	2

What is the Answer?

S₁₅ = 240

How does the Arithmetic and Geometric and Harmonic Sequences Calculator work?

Free Arithmetic and Geometric and Harmonic Sequences Calculator - This will take an arithmetic series or geometric series or harmonic series, and an optional amount (n), and determine the following information about the sequence
1) Explicit Formula
2) The remaining terms of the sequence up to (n)
3) The sum of the first (n) terms of the sequence Also known as arithmetic sequence, geometric sequence, and harmonic sequence
This calculator has 4 inputs.

What 1 formula is used for the Arithmetic and Geometric and Harmonic Sequences Calculator?

a_n = a₁ + (n - 1)d

For more math formulas, check out our Formula Dossier

What 5 concepts are covered in the Arithmetic and Geometric and Harmonic Sequences Calculator?

arithmetic and geometric and harmonic sequences
difference: the result of one of the important mathematical operations, which is obtained by subtracting two numbers
formula: a fact or a rule written with mathematical symbols. A concise way of expressing information symbolically.
sequence: an arrangement of numbers or collection or objects in a particular order
series: the cumulative sum of a given sequence of terms

Example calculations for the Arithmetic and Geometric and Harmonic Sequences Calculator

{1, 9, 17, 25, . . .}

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Arithmetic and Geometric and Harmonic Sequences Calculator