Question

Write an equation for the nth term of the arithmetic sequence. Then find a10.

10,0,−10,−20,..

Answer 1

The equation for the nth term of an arithmetic sequence is a_n = a_1 + (n - 1)d. The 10th term of the sequence is -80.

Step-by-step explanation:

An arithmetic sequence is a sequence of numbers in which the difference between any two consecutive terms is constant. To find the equation for the nth term of an arithmetic sequence, we can use the formula:

an = a1 + (n - 1)d

Where an represents the nth term, a1 is the first term, n is the position of the term, and d is the common difference. In this case, the first term (a1) is 10 and the common difference (d) is -10. So, the equation for the nth term is:

an = 10 + (n - 1)(-10)

To find a10, substitute n = 10 into the equation:

a10 = 10 + (10 - 1)(-10)

a10 = 10 + 9(-10)

a10 = 10 - 90

a10 = -80