A sequence is generated in which each term is 5 less than the previous term. If the twentieth term is -32, what is the fifteenth term ?
a. -57
b. -12
c. -7
d. 2
e. 7
please answer and explain
There are 5 terms between T15 and T20, so we need to add 5 five times to back up from T20 to T15.
-32 + 5(5) = -7
What is the 8th term in this sequence 9,4, -1,-6,-11
To find the fifteenth term of the sequence, we need to understand the pattern and the rule that governs the sequence.
Let's denote the first term of the sequence as "a" and find the general formula for the terms:
The first term: a
The second term: a - 5
The third term: (a - 5) - 5 = a - 10
The fourth term: (a - 10) - 5 = a - 15
We can see a pattern emerge, where each term is obtained by subtracting 5 from the previous term. So, the general formula for the sequence can be expressed as:
n-th term = a - 5(n-1), where "n" represents the position of the term in the sequence.
Now, let's find the value of "a" using the given information that the twentieth term is -32:
20th term = a - 5(20-1) (using the general formula)
-32 = a - 5(19)
-32 = a - 95
a = -32 + 95
a = 63
Now that we have the value of "a," we can find the fifteenth term by substituting "n = 15" into the general formula:
15th term = a - 5(15 - 1)
15th term = 63 - 5(14)
15th term = 63 - 70
15th term = -7
Therefore, the fifteenth term of the sequence is -7.
The correct answer is option c. -7.
To find the fifteenth term, we need to determine the common difference between the terms of the sequence.
Given that each term is 5 less than the previous term, the common difference between consecutive terms is -5.
To find the fifteenth term, we can use the formula for the nth term of an arithmetic sequence:
An = A1 + (n - 1)d
Where:
An is the nth term
A1 is the first term
d is the common difference
n is the position of the term
In this case, we can substitute the given values into the formula:
An = A1 + (n - 1)d
A15 = A1 + (15 - 1)(-5)
Since the twentieth term is -32, we can also find the first term (A1) as follows:
An = A1 + (n - 1)d
A20 = A1 + (20 - 1)(-5)
-32 = A1 + 19(-5)
Simplifying the equation:
-32 = A1 - 95
A1 = -32 + 95
A1 = 63
Now that we know A1, we can substitute it back into the formula to find the fifteenth term:
A15 = A1 + (15 - 1)(-5)
A15 = 63 + 14(-5)
A15 = 63 - 70
A15 = -7
Therefore, the fifteenth term is -7.
The correct answer is option c. -7.