Question

In an arithmetic sequence where a7 = -19 and a19 = -55, what's the formula for the nth term and what is the 31st term?

a) The formula for the nth term is a(n) = -19 - 2(n - 7).
b) The formula for the nth term is a(n) = -19 - 3(n - 7).
c) The formula for the nth term is a(n) = -19 + 3(n - 7).
d) The 31st term is a(31) = -61.

Answer 1

The formula for the nth term in an arithmetic sequence is a(n) = a(1) + (n-1)d, where a(1) is the first term and d is the common difference. The 31st term in the given sequence is -102.

Step-by-step explanation:

In an arithmetic sequence, the nth term can be found using the formula:
a(n) = a(1) + (n-1)d

Where a(n) is the nth term, a(1) is the first term, and d is the common difference.

Given that a(7) = -19 and a(19) = -55, we can substitute these values into the formula to find d:

-19 = a(1) + (7-1)d

-55 = a(1) + (19-1)d

Solving these equations gives us a(1) = -12 and d = -3.

Now we can find the 31st term using the formula:

a(31) = -12 + (31-1)(-3)

a(31) = -12 + 30(-3)

a(31) = -12 - 90

a(31) = -102