# Arithmetic and Geometric and Harmonic Sequences Calculator

Determine SequenceExpand Sequence
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<-- (Optional) Number of Expansion terms
<-- Enter First term a1
<-- Enter d

Calculate the explicit formula, term number 10, and the sum of the first 10 terms for the following arithmetic series:
{1,9,17,25,...}

The explicit formula for an arithmetic series is an = a1 + (n - 1)d
d represents the common difference between each term, an - an - 1
Looking at all the terms, we see the common difference is 8, and we have a1 = 1
Therefore, our explicit formula is an = 1 + 8(n - 1)

Calculate Terms (5 - 10)
Using our explicit formula with n = 10 and d = 8, we have:
Term #Math Step 1Math Step 2Math Step 3Term
5a5 = 1 + 8(5 - 1)a5 = 1 + 8(4)a5 = 1 + 32a5 = 33
6a6 = 1 + 8(6 - 1)a6 = 1 + 8(5)a6 = 1 + 40a6 = 41
7a7 = 1 + 8(7 - 1)a7 = 1 + 8(6)a7 = 1 + 48a7 = 49
8a8 = 1 + 8(8 - 1)a8 = 1 + 8(7)a8 = 1 + 56a8 = 57
9a9 = 1 + 8(9 - 1)a9 = 1 + 8(8)a9 = 1 + 64a9 = 65
10a10 = 1 + 8(10 - 1)a10 = 1 + 8(9)a10 = 1 + 72a10 = 73

Calculate the sum of the first 10 terms of the sequence, denoted Sn:
 Sn = n(a1 + an) 2

With n = 10, we get:
 S10 = 10(a1 + a10) 2

 S10 = 10(1 + 73) 2

 S10 = 10(74) 2

 S10 = 740 2

S10 = 370