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 |
Final Answer
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
