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

a_{n} = a_{1} + (n - 1)d

Define d

d = Δ between consecutive terms d = a_{n} - a_{n - 1}

We see a common difference = 2 We have a_{1} = 2 a_{n} = 2 + 2(n - 1)

Calculate Term (6)

Plug in n = 6 and d = 2 a_{6} = 2 + 2(6 - 1) a_{6} = 2 + 2(6 - 1) a_{6} = 2 + 2(5) a_{6} = 2 + 10 a_{6} = 12

Calculate Term (7)

Plug in n = 7 and d = 2 a_{7} = 2 + 2(7 - 1) a_{7} = 2 + 2(7 - 1) a_{7} = 2 + 2(6) a_{7} = 2 + 12 a_{7} = 14

Calculate Term (8)

Plug in n = 8 and d = 2 a_{8} = 2 + 2(8 - 1) a_{8} = 2 + 2(8 - 1) a_{8} = 2 + 2(7) a_{8} = 2 + 14 a_{8} = 16

Calculate Term (9)

Plug in n = 9 and d = 2 a_{9} = 2 + 2(9 - 1) a_{9} = 2 + 2(9 - 1) a_{9} = 2 + 2(8) a_{9} = 2 + 16 a_{9} = 18

Calculate Term (10)

Plug in n = 10 and d = 2 a_{10} = 2 + 2(10 - 1) a_{10} = 2 + 2(10 - 1) a_{10} = 2 + 2(9) a_{10} = 2 + 18 a_{10} = 20

Calculate Term (11)

Plug in n = 11 and d = 2 a_{11} = 2 + 2(11 - 1) a_{11} = 2 + 2(11 - 1) a_{11} = 2 + 2(10) a_{11} = 2 + 20 a_{11} = 22

Calculate Term (12)

Plug in n = 12 and d = 2 a_{12} = 2 + 2(12 - 1) a_{12} = 2 + 2(12 - 1) a_{12} = 2 + 2(11) a_{12} = 2 + 22 a_{12} = 24

Calculate Term (13)

Plug in n = 13 and d = 2 a_{13} = 2 + 2(13 - 1) a_{13} = 2 + 2(13 - 1) a_{13} = 2 + 2(12) a_{13} = 2 + 24 a_{13} = 26

Calculate Term (14)

Plug in n = 14 and d = 2 a_{14} = 2 + 2(14 - 1) a_{14} = 2 + 2(14 - 1) a_{14} = 2 + 2(13) a_{14} = 2 + 26 a_{14} = 28

Calculate Term (15)

Plug in n = 15 and d = 2 a_{15} = 2 + 2(15 - 1) a_{15} = 2 + 2(15 - 1) a_{15} = 2 + 2(14) a_{15} = 2 + 28 a_{15} = 30

Calculate S_{n}:

S_{n} = Sum of the first n terms

S_{n} =

n(a_{1} + a_{n})

2

Substituting n = 15, we get:

S_{15} =

15(a_{1} + a_{15})

2

S_{15} =

15(2 + 30)

2

S_{15} =

15(32)

2

S_{15} =

480

2

S_{15} = 240

What is the Answer?

S_{15} = 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?