Find a₁₃ of the sequence (-1, 38, 77, ...)
Formula:
[tex]a_n = a_1 + (n-1)d[/tex]
Given:
[tex]a_1 = -1[/tex]
[tex]d = 38 - (-1) = 39[/tex]
Solution:
[tex]a_{13} = a_1 + (13-1)d[/tex]
[tex]a_{13} = -1 + (12)(39)[/tex]
Answer:
[tex]a_{13} = 467[/tex]
Answer (1)
The 13th term a 13 of the sequence is 467. ; To find the 13th term a 13 of the given arithmetic sequence, we will use the formula for the n -th term of an arithmetic sequence:
a n = a 1 + ( n − 1 ) × d
Here, a 1 represents the first term of the sequence, n is the term number we want to find, and d is the common difference between consecutive terms in the sequence.
Given:
First term, a 1 = − 1
Common difference, d = 38 − ( − 1 ) = 39
Calculation: To find the 13th term, plug the known values into the formula:
a 13 = a 1 + ( 13 − 1 ) × d a 13 = − 1 + ( 12 ) × 39
Calculate the expression step-by-step:
Subtract 1 from 13, which gives:
12
Multiply 12 by the common difference 39:
12 × 39 = 468
Finally, add this result to a 1 :
− 1 + 468 = 467
