Question

Find the sum of the first 32 terms of the arithmetic sequence with the given first term and common difference:

a1 = 10; d = -2

Answer 1

The sum of the first 32 terms of an arithmetic sequence with a first term of 10 and a common difference of -2 is -672.

Step-by-step explanation:

The student is asking for the sum of the first 32 terms of an arithmetic sequence. The formula to find the sum of the first n terms of an arithmetic sequence is:

Sn = ½ n (2a1 + (n - 1)d)

where Sn is the sum of the first n terms,

a1 is the first term,

d is the common difference, and

n is the number of terms.

To solve the problem with the given a1 = 10 and d = -2 for n = 32, plug the values into the formula:

S32 = ½ × 32 (2 × 10 + (32 - 1) × -2)

S32 = 16 (20 + 31 × -2)

S32 = 16 (20 - 62)

S32 = 16 (-42)

S32 = -672

So, the sum of the first 32 terms of the sequence is -672.