Arithmetic and Geometric and Harmonic Sequences Calculator
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Calculate the explicit formula term number 10 Sum of the first 10 terms for: 3,12,48
The explicit formula for a geometric series is an = a1r(n - 1) r represents the common ratio between each term below:
r =
an
an - 1
Looking at all the terms, we see the common ratio (r) is 4, and we have a1 = 3 We simplify a1 to just a ar = 3 x 4 = Therefore, our explicit formula is an = (3)4(n - 1)
Calculate Terms (4 - 10)
Plug in n = 10 and r = 4
#
Step 1
Step 2
Step 3
Term
a4
3 x 4(4 - 1)
3 x 43
3 x 64
192
a5
3 x 4(5 - 1)
3 x 44
3 x 256
768
a6
3 x 4(6 - 1)
3 x 45
3 x 1024
3072
a7
3 x 4(7 - 1)
3 x 46
3 x 4096
12288
a8
3 x 4(8 - 1)
3 x 47
3 x 16384
49152
a9
3 x 4(9 - 1)
3 x 48
3 x 65536
196608
a10
3 x 4(10 - 1)
3 x 49
3 x 262144
786432
Calculate the sum of the first 10 terms of the sequence, denoted Sn:
Sn =
a1(1 - rn)
1 - r
With n = 10, and r = 4, we get:
S10 =
3(1 - 410)
1 - 4
S10 =
3(1 - 1048576)
-3
S10 =
3(-1048575)
-3
S10 =
-3145725
-3
S10 = 1048575
You have 2 free calculationss remaining
What is the Answer?
S10 = 1048575
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?