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

an = a1 + (n - 1)d

Define d

d = Δ between consecutive terms

d = an - an - 1

We see a common difference = 60

We have a1 = 638

an = 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 Sn:

Sn = Sum of the first n terms

Sn =	n(a1 + an)
	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 sequencesdifferencethe result of one of the important mathematical operations, which is obtained by subtracting two numbersformulaa fact or a rule written with mathematical symbols. A concise way of expressing information symbolically.sequencean arrangement of numbers or collection or objects in a particular orderseriesthe cumulative sum of a given sequence of terms

Example calculations for the Arithmetic and Geometric and Harmonic Sequences Calculator