Write a formula for the general term (the nth term) of the arithmetic sequence shown below. Do not use a recursion formula. Then use the formula for a'n to find a20, the 20th term of the sequence.
a'1 = -13, d = -5
well, for any A.P., the nth term, Tn is
Tn = a + (n-1)d
So, plug in your numbers.
To find the formula for the general term (the nth term) of an arithmetic sequence, we can use the formula:
a'n = a'1 + (n - 1) * d
where a'n is the nth term, a'1 is the first term, n is the term number, and d is the common difference.
Given that a'1 = -13 and d = -5, we can substitute these values into the formula:
a'n = -13 + (n - 1) * (-5)
To find the 20th term (a20), we can substitute n = 20 into the formula:
a20 = -13 + (20 - 1) * (-5)
Simplifying the expression:
a20 = -13 + 19 * (-5)
a20 = -13 - 95
a20 = -108
Therefore, the 20th term (a20) of the given arithmetic sequence is -108.
To find the formula for the general term (nth term) of an arithmetic sequence, you can use the following formula:
a'n = a'1 + (n - 1) * d
Where:
- a'n represents the nth term of the sequence.
- a'1 represents the first term of the sequence.
- d represents the common difference between each term.
In this case, the given values are a'1 = -13 and d = -5.
Plugging these values into the formula, we get:
a'n = -13 + (n - 1) * (-5)
Simplifying this expression, we have:
a'n = -13 - 5n + 5
Combining like terms, we get the following formula for the nth term of the sequence:
a'n = -8 - 5n
To find a20, the 20th term of the sequence, we substitute n = 20 into the formula:
a'20 = -8 - 5(20)
a'20 = -8 - 100
a'20 = -108
Therefore, the 20th term of the sequence is -108.