How to find the nth term of an arithmetic sequence - GRE Quantitative Reasoning
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The first term in a sequence of integers is 2 and the second term is 10. All subsequent terms are the arithmetic mean of all of the preceding terms. What is the 39th term?
The first term in a sequence of integers is 2 and the second term is 10. All subsequent terms are the arithmetic mean of all of the preceding terms. What is the 39th term?
The first term and second term average out to 6. So the third term is 6. Now add 6 to the preceding two terms and divide by 3 to get the average of the first three terms, which is the value of the 4th term. This, too, is 6 (18/3)—all terms after the 2nd are 6, including the 39th. Thus, the answer is 6.
The first term and second term average out to 6. So the third term is 6. Now add 6 to the preceding two terms and divide by 3 to get the average of the first three terms, which is the value of the 4th term. This, too, is 6 (18/3)—all terms after the 2nd are 6, including the 39th. Thus, the answer is 6.
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In a sequence of numbers, the first two values are 1 and 2. Each successive integer is calculated by adding the previous two and mutliplying that result by 3. What is fifth value in this sequence?
In a sequence of numbers, the first two values are 1 and 2. Each successive integer is calculated by adding the previous two and mutliplying that result by 3. What is fifth value in this sequence?
Our sequence begins as 1, 2.
Element 3: (Element 1 + Element 2) * 3 = (1 + 2) * 3 = 3 * 3 = 9
Element 4: (Element 2 + Element 3) * 3 = (2 + 9) * 3 = 11 * 3 = 33
Element 5: (Element 3 + Element 4) * 3 = (9 + 33) * 3 = 42 * 3 = 126
Our sequence begins as 1, 2.
Element 3: (Element 1 + Element 2) * 3 = (1 + 2) * 3 = 3 * 3 = 9
Element 4: (Element 2 + Element 3) * 3 = (2 + 9) * 3 = 11 * 3 = 33
Element 5: (Element 3 + Element 4) * 3 = (9 + 33) * 3 = 42 * 3 = 126
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Consider the following sequence of integers:
5, 11, 23, 47
What is the 6th element in this sequence?
Consider the following sequence of integers:
5, 11, 23, 47
What is the 6th element in this sequence?
First, consider the change in each element. Notice that in each case, a given element is twice the preceding one plus one:
11 = 2 * 5 + 1
23 = 11 * 2 + 1
47 = 23 * 2 + 1
To find the 6th element, continue following this:
The 5th: 47 * 2 + 1 = 95
The 6th: 95 * 2 + 1 = 191
First, consider the change in each element. Notice that in each case, a given element is twice the preceding one plus one:
11 = 2 * 5 + 1
23 = 11 * 2 + 1
47 = 23 * 2 + 1
To find the 6th element, continue following this:
The 5th: 47 * 2 + 1 = 95
The 6th: 95 * 2 + 1 = 191
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The sequence 
begins with the numbers 
and has the 
term defined as 
, for 
.
What is the value of the 
term of the sequence?
The sequence
What is the value of the
The first term of the sequence is 
, so here 
, and we're interested in finding the 20th term, so we'll use n = 20.
Plugging these values into the given expression for the nth term gives us our answer.
and 
The first term of the sequence is
Plugging these values into the given expression for the nth term gives us our answer.
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Let Z represent a sequence of numbers 
wherein each term is defined as seven less than three times the preceding term. If 
, what is the first term in the sequence?
Let Z represent a sequence of numbers
Let us first write the value of a consecutive term in a numerical format:
Consequently,
Using the first equation, we can define 
in terms of 
:
This allows us to rewrite
as
Rearrangement of terms allows us to solve for 
:
Now, using our second equation, we can find 
, the first term:
Let us first write the value of a consecutive term in a numerical format:
Consequently,
Using the first equation, we can define
This allows us to rewrite
as
Rearrangement of terms allows us to solve for
Now, using our second equation, we can find
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