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Geometric sequences and series juniorg8.com Topical summary | Algebra 2 synopsis | MathBits" Teacher resources Terms of Use call Person: Donna Roberts
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Some sequences room composed of just random values, if others have actually a identify pattern that is used to come at the sequence"s terms. The geometric sequence, for example, is based ~ above the multiplication of a constant value to come at the following term in the sequence.

You are watching: What is the sum of the first seven terms of the geometric series? 3 + 12 + 48 + 192 + ...


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Geometric sequences have actually a non-linear nature once graphed (as a scatter plot). The domain is composed of the counting numbers 1, 2, 3, 4, ... (representing the place of each term) and the range consists of the actual regards to the sequence. In the graph displayed above, while the x-axis rises by a constant value of one, the y value increases by a consistent multiple the 2.

Geometric assignment


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Multiply

Geometric sequences monitor a pattern of multiplying a resolved amount (not zero) native one term to the next. The number being multiplied each time is continuous (always the same). a1, (a1r), (a1r2), (a1r3), (a1r4), ...

The solved amount is called the common ratio, r, referring come the fact that the ratio (fraction) of second term come the very first term yields the common multiple. To discover the usual ratio, divide the second term by the very first term.


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Geometric Sequence: Common Ratio, r:

r = 4. A 4 is multiply times each term to come at the following term. OR ... Division a2 by a1 to discover the usual ratio the 4.
r = -3. A -3 is multiplied times every term to arrive at the next term. OR ... Divide a2 by a1 to find the typical ratio that -3.
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A 2/3 is multiplied times each term to arrive at the following term.OR ... Divide a2 through a1 to uncover the typical ratio of 2/3.

When the regards to a sequence are added together, the sum is described as a series. We will be working through finite sums (the amount of a specific number of terms).


Geometric Series: Sn = a1 + (a1r) + (a1r2) +(a1r3) + (a1r4) + ... + (a1rn - 1) A geometric collection is the adding together that the terms of a geometric sequence.
To find any type of term that a geometric sequence:
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wherein a1 is the first term that the sequence, r is the usual ratio,n is the number of the term to find.

See more: What Does Hildegard Name Meaning, What Does Hildegard Mean


To find the sum that a certain number of terms the a geometric sequence:
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where Sn is the amount of n terms (nth partial sum), a1 is the an initial term, r is the typical ratio.

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Let"s take it a look at a range of examples working with geometric sequences and series. read the "Answers" closely to uncover "hints" regarding how to address these questions.