Question

Find the 22nd term.

1, 4, 7, 10, 13, ...
Enter the number that belongs in the green box.
1 + 3([ ? ] − 1)
1st term + common difference(desired term - 1)
Enter

Answer 1

Answer: The sequence has a common difference of 3, since each term is 3 more than the previous one. To find the 22nd term, we can use the formula for the nth term of an arithmetic sequence:

a_n = a_1 + (n-1)d

where a_1 is the first term, d is the common difference, and n is the term number we want to find.

In this case, we have:

a_1 = 1 (the first term)

d = 3 (the common difference)

n = 22 (the term number we want to find)

Substituting these values into the formula, we get:

a_22 = 1 + (22-1)3

= 1 + 21*3

= 64

Therefore, the 22nd term is 64.

Using the formula for the nth term, we can also check that the sequence up to the 22nd term is:

1, 4, 7, 10, 13, 16, 19, 22, 25, 28, 31, 34, 37, 40, 43, 46, 49, 52, 55, 58, 61, 64.

Explanation:

Answer 2

Answer:

The 22nd term is 64.

The number belonging to the green box is 22

Explanation:

Using the formula for the nth term of an arithmetic sequence:

an = a1 + (n-1)d

where:
an = desired term
a1 = first term
d = common difference

We have:
a1 = 1
d = 3

To find the 22nd term, we substitute n = 22 into the formula:

a22 = 1 + (22 - 1)3
a22 = 1 + 21*3
a22 = 1 + 63
a22 = 64

Therefore, the 22nd term is 64.

The number that belongs in the green box is 22.

1 + 3(22 - 1) = 64