Arithmetic and Geometric and Harmonic Sequences Calculator
Calculate the explicit formula Calculate term number 15 And the Sum of the first 15 terms for: 2,4,6,8,10
Explicit Formula
an = a1 + (n - 1)d
Define d
d = Δ between consecutive terms d = an - an - 1
We see a common difference = 2 We have a1 = 2 an = 2 + 2(n - 1)
Calculate Term (6)
Plug in n = 6 and d = 2 a6 = 2 + 2(6 - 1) a6 = 2 + 2(6 - 1) a6 = 2 + 2(5) a6 = 2 + 10 a6 = 12
Calculate Term (7)
Plug in n = 7 and d = 2 a7 = 2 + 2(7 - 1) a7 = 2 + 2(7 - 1) a7 = 2 + 2(6) a7 = 2 + 12 a7 = 14
Calculate Term (8)
Plug in n = 8 and d = 2 a8 = 2 + 2(8 - 1) a8 = 2 + 2(8 - 1) a8 = 2 + 2(7) a8 = 2 + 14 a8 = 16
Calculate Term (9)
Plug in n = 9 and d = 2 a9 = 2 + 2(9 - 1) a9 = 2 + 2(9 - 1) a9 = 2 + 2(8) a9 = 2 + 16 a9 = 18
Calculate Term (10)
Plug in n = 10 and d = 2 a10 = 2 + 2(10 - 1) a10 = 2 + 2(10 - 1) a10 = 2 + 2(9) a10 = 2 + 18 a10 = 20
Calculate Term (11)
Plug in n = 11 and d = 2 a11 = 2 + 2(11 - 1) a11 = 2 + 2(11 - 1) a11 = 2 + 2(10) a11 = 2 + 20 a11 = 22
Calculate Term (12)
Plug in n = 12 and d = 2 a12 = 2 + 2(12 - 1) a12 = 2 + 2(12 - 1) a12 = 2 + 2(11) a12 = 2 + 22 a12 = 24
Calculate Term (13)
Plug in n = 13 and d = 2 a13 = 2 + 2(13 - 1) a13 = 2 + 2(13 - 1) a13 = 2 + 2(12) a13 = 2 + 24 a13 = 26
Calculate Term (14)
Plug in n = 14 and d = 2 a14 = 2 + 2(14 - 1) a14 = 2 + 2(14 - 1) a14 = 2 + 2(13) a14 = 2 + 26 a14 = 28
Calculate Term (15)
Plug in n = 15 and d = 2 a15 = 2 + 2(15 - 1) a15 = 2 + 2(15 - 1) a15 = 2 + 2(14) a15 = 2 + 28 a15 = 30
Calculate Sn:
Sn = Sum of the first n terms
Sn =
n(a1 + an)
2
Substituting n = 15, we get:
S15 =
15(a1 + a15)
2
S15 =
15(2 + 30)
2
S15 =
15(32)
2
S15 =
480
2
S15 = 240
What is the Answer?
S15 = 240
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?