Arithmetic and Geometric and Harmonic Sequences Calculator

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Calculate the explicit formula

Calculate term number 15

And the Sum of the first 15 terms for:

1,2,3,4,5

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 = 1

We have a₁ = 1

a_n = 1 + 1(n - 1)

Calculate Term (6)

Plug in n = 6 and d = 1

a₆ = 1 + 1(6 - 1)

a₆ = 1 + 1(6 - 1)

a₆ = 1 + 1(5)

a₆ = 1 + 5

a₆ = 6

Calculate Term (7)

Plug in n = 7 and d = 1

a₇ = 1 + 1(7 - 1)

a₇ = 1 + 1(7 - 1)

a₇ = 1 + 1(6)

a₇ = 1 + 6

a₇ = 7

Calculate Term (8)

Plug in n = 8 and d = 1

a₈ = 1 + 1(8 - 1)

a₈ = 1 + 1(8 - 1)

a₈ = 1 + 1(7)

a₈ = 1 + 7

a₈ = 8

Calculate Term (9)

Plug in n = 9 and d = 1

a₉ = 1 + 1(9 - 1)

a₉ = 1 + 1(9 - 1)

a₉ = 1 + 1(8)

a₉ = 1 + 8

a₉ = 9

Calculate Term (10)

Plug in n = 10 and d = 1

a₁₀ = 1 + 1(10 - 1)

a₁₀ = 1 + 1(10 - 1)

a₁₀ = 1 + 1(9)

a₁₀ = 1 + 9

a₁₀ = 10

Calculate Term (11)

Plug in n = 11 and d = 1

a₁₁ = 1 + 1(11 - 1)

a₁₁ = 1 + 1(11 - 1)

a₁₁ = 1 + 1(10)

a₁₁ = 1 + 10

a₁₁ = 11

Calculate Term (12)

Plug in n = 12 and d = 1

a₁₂ = 1 + 1(12 - 1)

a₁₂ = 1 + 1(12 - 1)

a₁₂ = 1 + 1(11)

a₁₂ = 1 + 11

a₁₂ = 12

Calculate Term (13)

Plug in n = 13 and d = 1

a₁₃ = 1 + 1(13 - 1)

a₁₃ = 1 + 1(13 - 1)

a₁₃ = 1 + 1(12)

a₁₃ = 1 + 12

a₁₃ = 13

Calculate Term (14)

Plug in n = 14 and d = 1

a₁₄ = 1 + 1(14 - 1)

a₁₄ = 1 + 1(14 - 1)

a₁₄ = 1 + 1(13)

a₁₄ = 1 + 13

a₁₄ = 14

Calculate Term (15)

Plug in n = 15 and d = 1

a₁₅ = 1 + 1(15 - 1)

a₁₅ = 1 + 1(15 - 1)

a₁₅ = 1 + 1(14)

a₁₅ = 1 + 14

a₁₅ = 15

Calculate S_n:

S_n = Sum of the first n terms

Substituting n = 15, we get:

You have 2 free calculationss remaining

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Tags:

• arithmetic and geometric and harmonic sequences
• difference
• formula
• sequence
• series