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(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(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(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(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(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(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(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 |
You have 2 free calculationss remaining
What is the Answer?
How does the Arithmetic and Geometric and Harmonic Sequences Calculator work?
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
Arithmetic and Geometric and Harmonic Sequences Calculator Video
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