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What is the 7th term of the geometric sequence where a1 equals 1024 and a4 equals -16?
Given:
a1=1024
a4=-16
Find: a7
Formula:
an=a1rn-1
To get the ratio, r:
a4=a1r4-1
-16=1024r4-1
-16=1024r3
-16/1024=1024/1024r3
-1/64=r3
-1/4=r
Substiture r=1/4 to the formula to get a7
a7=a1r7-1
=a1r6
=1024(-1/4)6
=1024(1/4096)
=1/4
=0.25
Therefore the 7th term=0.25
FromC2H5.OH:
The fourth term is the geometric mean of the first and seventh terms and is therefore the square root of their product;
this means that -16 squared = 1024 x a7
ie a7 = 256/1024 = 0.25
What else can I help you with?
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What does geometric sequence?
You mean what IS a geometric sequence? It's when the ratio of the terms is constant, meaning: 1, 2, 4, 8, 16... The ratio of one term to the term directly following it is always 1:2, or .5. So like, instead of an arithmetic sequence, where you're adding a specific amount each time, in a geometric sequence, you're multiplying by that term.
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What is geometric sequence in math mean?
A geometric sequence is a sequence of numbers where each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio. For example, in the sequence 2, 6, 18, 54, the common ratio is 3. The general form of a geometric sequence can be expressed as ( a_n = a_1 \cdot r^{(n-1)} ), where ( a_1 ) is the first term, ( r ) is the common ratio, and ( n ) is the term number.
Is geometric sequence a sequence in which each successive terms of the sequence are in equal ratio?
Yes, that's what a geometric sequence is about.
What is the nth term of the geometric sequence 4 8 16 32 ...?
The given sequence is a geometric sequence where each term is multiplied by 2 to get the next term. The first term (a) is 4, and the common ratio (r) is 2. The nth term of a geometric sequence can be found using the formula ( a_n = a \cdot r^{(n-1)} ). Therefore, the nth term of this sequence is ( 4 \cdot 2^{(n-1)} ).
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Each number in the sequence is the previous number divided by 4. Therefore the 7th term starting from 1024 is 0.25. The first 8 terms are: 1024, 256, 64, 16, 4, 1, 0.25 and 0.0625.
What does geometric sequence?
You mean what IS a geometric sequence? It's when the ratio of the terms is constant, meaning: 1, 2, 4, 8, 16... The ratio of one term to the term directly following it is always 1:2, or .5. So like, instead of an arithmetic sequence, where you're adding a specific amount each time, in a geometric sequence, you're multiplying by that term.
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This is a geometric sequence since there is a common ratio between each term. In this case, multiplying the previous term in the sequence by 10.
Is this arithmetic or geometric 2 4 8 16?
The sequence 2, 4, 8, 16 is a geometric sequence. In a geometric sequence, each term is obtained by multiplying the previous term by a constant factor. In this case, each term is multiplied by 2 (2 × 2 = 4, 4 × 2 = 8, 8 × 2 = 16).
What is the difference between an arithmetic sequence and a geometric sequence?
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