Arithmetic and Geometric and Harmonic Sequences Calculator

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Calculate the explicit formula

Calculate term number 10

And the Sum of the first 10 terms for:

638,698,758

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 = 60

We have a₁ = 638

a_n = 638 + 60(n - 1)

Calculate Term (4)

Plug in n = 4 and d = 60

a₄ = 638 + 60(4 - 1)

a₄ = 638 + 60(3)

a₄ = 638 + 180

a₄ = 818

Calculate Term (5)

Plug in n = 5 and d = 60

a₅ = 638 + 60(5 - 1)

a₅ = 638 + 60(4)

a₅ = 638 + 240

a₅ = 878

Calculate Term (6)

Plug in n = 6 and d = 60

a₆ = 638 + 60(6 - 1)

a₆ = 638 + 60(5)

a₆ = 638 + 300

a₆ = 938

Calculate Term (7)

Plug in n = 7 and d = 60

a₇ = 638 + 60(7 - 1)

a₇ = 638 + 60(6)

a₇ = 638 + 360

a₇ = 998

Calculate Term (8)

Plug in n = 8 and d = 60

a₈ = 638 + 60(8 - 1)

a₈ = 638 + 60(7)

a₈ = 638 + 420

a₈ = 1058

Calculate Term (9)

Plug in n = 9 and d = 60

a₉ = 638 + 60(9 - 1)

a₉ = 638 + 60(8)

a₉ = 638 + 480

a₉ = 1118

Calculate Term (10)

Plug in n = 10 and d = 60

a₁₀ = 638 + 60(10 - 1)

a₁₀ = 638 + 60(9)

a₁₀ = 638 + 540

a₁₀ = 1178

Calculate S_n:

S_n = Sum of the first n terms

S_n =	n(a₁ + a_n)
	2

Substituting n = 10, we get:

S₁₀ =	10(a₁ + a₁₀)
	2

S₁₀ =	10(638 + 1178)
	2

S₁₀ =	10(1816)
	2

S₁₀ =	18160
	2

Final Answer

S₁₀ = 9080

You have 1 free calculations remaining

What is the Answer?

S₁₀ = 9080

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?

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