What is the sum of the arithmetic sequence 8, 14, 20 if there are 22 terms?

To find the sum of the arithmetic sequence, we first need to determine the first term, common difference, and the total number of terms.

The first term (a) is 8. The common difference (d) can be calculated by subtracting the first term from the second term:

d = 14 – 8 = 6.

Now that we have a and d, we can use the formula for the sum (S) of the first n terms of an arithmetic sequence:

S_n = rac{n}{2} (2a + (n – 1)d)

In this case, n = 22, a = 8, and d = 6. Plugging in these values:

S₂₂ = rac{22}{2} (2(8) + (22 – 1)6)

This simplifies to:

S₂₂ = 11 (16 + 21 imes 6)

= 11 (16 + 126)

= 11 imes 142

= 1562

So, the sum of the first 22 terms of the arithmetic sequence is 1562.