Find the 24th term (a_24) of the sequence: 3, -30, -63, ...
Formula: a_n = a_1 + (n - 1)d
Given:
- First term, a_1 = 3
- Common difference, d = -33 (since -30 - 3 = -33)
- Term number, n = 24
Solution:
a_24 = a_1 + (24 - 1)d
= 3 + 23(-33)
= 3 - 759
= -756
Answer: a_24 = -756
Answer (1)
To find the 24th term a 24 of the given arithmetic sequence, we can use the formula for the n -th term of an arithmetic sequence:
a n = a 1 + ( n − 1 ) ⋅ d
Where:
a 1 is the first term of the sequence.
d is the common difference between the terms.
n is the term number we want to find.
Given in the problem:
First term, a 1 = 3
Common difference, d = − 33 (calculated as − 30 − 3 = − 33 )
The term number we want, n = 24
We substitute these values into the formula:
a 24 = 3 + ( 24 − 1 ) ( − 33 )
First, simplify inside the parentheses:
24 − 1 = 23
Substitute back in:
a 24 = 3 + 23 ⋅ ( − 33 )
Calculate 23 ⋅ ( − 33 ) :
23 ⋅ ( − 33 ) = − 759
Substitute that back in:
a 24 = 3 − 759
Finally, calculate 3 − 759 :
a 24 = − 756
So, the 24th term of the sequence is a 24 = − 756 .
