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 |
Final Answer
S10 = 1048575
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.
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?
an = a1 + (n - 1)d
What 5 concepts are covered in the Arithmetic and Geometric and Harmonic Sequences Calculator?
- arithmetic and geometric and harmonic sequences
- difference
- the result of one of the important mathematical operations, which is obtained by subtracting two numbers
- formula
- a fact or a rule written with mathematical symbols. A concise way of expressing information symbolically.
- sequence
- an arrangement of numbers or collection or objects in a particular order
- series
- the cumulative sum of a given sequence of terms
