Question

Find a(33) if the first term in the sequence is 3 and the common difference is -1.

Option 1: -29
Option 2: 36
Option 3: -36
Option 4: -30

Answer 1

The 33rd term of the arithmetic sequence with a first term of 3 and a common difference of -1 is calculated using the formula. Substituting the given values, we find that a(33) = -29, which matches Option 1.

Step-by-step explanation:

The sequence in question is an arithmetic sequence, where the first term (a1) is 3, and the common difference (d) is -1. To find the 33rd term of this sequence (a(33)), we use the formula for the nth term of an arithmetic sequence, a(n) = a1 + (n - 1)*d. In this case, n is 33. Substituting these values into the formula gives us:

a(33) = 3 + (33 - 1)*(-1)

a(33) = 3 + 32*(-1)

a(33) = 3 - 32

a(33) = -29

Thus, the value of the 33rd term in the sequence is -29, which corresponds to Option 1.