Series and # terms1st Term &
Series Factor




Calculate the explicit formula

Calculate term number 10

And the Sum of the first 10 terms for:

152,170,188,206

Explicit Formula

an = a1 + (n - 1)d

Define d

d = Δ between consecutive terms

d = an - an - 1

We see a common difference = 18

We have a1 = 152

an = 152 + 18(n - 1)

Calculate Term (5)

Plug in n = 5 and d = 18

a5 = 152 + 18(5 - 1)

a5 = 152 + 18(5 - 1)

a5 = 152 + 18(4)

a5 = 152 + 72

a5 = 224

Calculate Term (6)

Plug in n = 6 and d = 18

a6 = 152 + 18(6 - 1)

a6 = 152 + 18(6 - 1)

a6 = 152 + 18(5)

a6 = 152 + 90

a6 = 242

Calculate Term (7)

Plug in n = 7 and d = 18

a7 = 152 + 18(7 - 1)

a7 = 152 + 18(7 - 1)

a7 = 152 + 18(6)

a7 = 152 + 108

a7 = 260

Calculate Term (8)

Plug in n = 8 and d = 18

a8 = 152 + 18(8 - 1)

a8 = 152 + 18(8 - 1)

a8 = 152 + 18(7)

a8 = 152 + 126

a8 = 278

Calculate Term (9)

Plug in n = 9 and d = 18

a9 = 152 + 18(9 - 1)

a9 = 152 + 18(9 - 1)

a9 = 152 + 18(8)

a9 = 152 + 144

a9 = 296

Calculate Term (10)

Plug in n = 10 and d = 18

a10 = 152 + 18(10 - 1)

a10 = 152 + 18(10 - 1)

a10 = 152 + 18(9)

a10 = 152 + 162

a10 = 314

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(152 + 314)
  2

S10  =  10(466)
  2

S10  =  4660
  2

Final Answer

S10 = 2330


You have 2 free calculationss remaining



What is the Answer?
S10 = 2330
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?

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
Example calculations for the Arithmetic and Geometric and Harmonic Sequences Calculator
  1. {1, 9, 17, 25, . . .}

Arithmetic and Geometric and Harmonic Sequences Calculator Video


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