Find the 40th term in each arithmetic sequence.
1. 4, 8, 12, 16, ...
2. 13, 26, 39, 52, ...
3. 6, 12, 18, 24, ...
40th term = 1st term + [39 * (2nd term - 1st term)]
13, 26, 39, 52
Jeioeoe
To find the 40th term in an arithmetic sequence, you can use the formula for the nth term of an arithmetic sequence:
nth term = first term + (n - 1) * common difference
Let's solve each sequence one by one:
1. For the sequence 4, 8, 12, 16, ...
In this sequence, the first term (a) is 4 and the common difference (d) is 8 - 4 = 4.
Using the formula, we can find the 40th term:
40th term = 4 + (40 - 1) * 4
= 4 + 39 * 4
= 4 + 156
= 160
Therefore, the 40th term in the sequence 4, 8, 12, 16, ... is 160.
2. For the sequence 13, 26, 39, 52, ...
In this sequence, the first term (a) is 13 and the common difference (d) is 26 - 13 = 13.
Using the formula, we can find the 40th term:
40th term = 13 + (40 - 1) * 13
= 13 + 39 * 13
= 13 + 507
= 520
Therefore, the 40th term in the sequence 13, 26, 39, 52, ... is 520.
3. For the sequence 6, 12, 18, 24, ...
In this sequence, the first term (a) is 6 and the common difference (d) is 12 - 6 = 6.
Using the formula, we can find the 40th term:
40th term = 6 + (40 - 1) * 6
= 6 + 39 * 6
= 6 + 234
= 240
Therefore, the 40th term in the sequence 6, 12, 18, 24, ... is 240.