 # Arithmetic and Geometric and Harmonic Sequences Calculator

Series and # terms1st Term &
Series Factor

Calculate the explicit formula
Calculate term number 10
And the Sum of the first 10 terms for:
{1,9,17,25}

## Explicit Formula

an = a1 + (n - 1)d

## Define d

d = Δ between consecutive terms
d = an - an - 1

We see a common difference = 8
We have a1 = 1
an = 1 + 8(n - 1)

## Calculate Term (5)

Plug in n = 5 and d = 8
a5 = 1 + 8(5 - 1)
a5 = 1 + 8(5 - 1)
a5 = 1 + 8(4)
a5 = 1 + 32
a5 = 33

## Calculate Term (6)

Plug in n = 6 and d = 8
a6 = 1 + 8(6 - 1)
a6 = 1 + 8(6 - 1)
a6 = 1 + 8(5)
a6 = 1 + 40
a6 = 41

## Calculate Term (7)

Plug in n = 7 and d = 8
a7 = 1 + 8(7 - 1)
a7 = 1 + 8(7 - 1)
a7 = 1 + 8(6)
a7 = 1 + 48
a7 = 49

## Calculate Term (8)

Plug in n = 8 and d = 8
a8 = 1 + 8(8 - 1)
a8 = 1 + 8(8 - 1)
a8 = 1 + 8(7)
a8 = 1 + 56
a8 = 57

## Calculate Term (9)

Plug in n = 9 and d = 8
a9 = 1 + 8(9 - 1)
a9 = 1 + 8(9 - 1)
a9 = 1 + 8(8)
a9 = 1 + 64
a9 = 65

## Calculate Term (10)

Plug in n = 10 and d = 8
a10 = 1 + 8(10 - 1)
a10 = 1 + 8(10 - 1)
a10 = 1 + 8(9)
a10 = 1 + 72
a10 = 73

## 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(1 + 73) 2

 S10  = 10(74) 2

 S10  = 740 2

S10 = 370

### 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?

1. an = 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