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:
1,5,9,13,17
Explicit Formula
an = a1 + (n - 1)d
Define d
d = Δ between consecutive terms
d = an - an - 1
We see a common difference = 4
We have a1 = 1
an = 1 + 4(n - 1)
Calculate Term (6)
Plug in n = 6 and d = 4
a6 = 1 + 4(6 - 1)
a6 = 1 + 4(6 - 1)
a6 = 1 + 4(5)
a6 = 1 + 20
a6 = 21
Calculate Term (7)
Plug in n = 7 and d = 4
a7 = 1 + 4(7 - 1)
a7 = 1 + 4(7 - 1)
a7 = 1 + 4(6)
a7 = 1 + 24
a7 = 25
Calculate Term (8)
Plug in n = 8 and d = 4
a8 = 1 + 4(8 - 1)
a8 = 1 + 4(8 - 1)
a8 = 1 + 4(7)
a8 = 1 + 28
a8 = 29
Calculate Term (9)
Plug in n = 9 and d = 4
a9 = 1 + 4(9 - 1)
a9 = 1 + 4(9 - 1)
a9 = 1 + 4(8)
a9 = 1 + 32
a9 = 33
Calculate Term (10)
Plug in n = 10 and d = 4
a10 = 1 + 4(10 - 1)
a10 = 1 + 4(10 - 1)
a10 = 1 + 4(9)
a10 = 1 + 36
a10 = 37
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 + 37)
2
S10 =
10(38)
2
S10 =
380
2
Final Answer
S10 = 190
You have 2 free calculationss remaining
What is the Answer?
S10 = 190
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?