Question

What is the arithmetic sequence of the first term being -12 and the fifth term being -.75

Answer 1

an = -12 + (n - 1) * 2.8125

Explanation:

Finding the common difference:

The formula for the nth term of an arithmetic sequence is given by:

`a_(n)=a_(1)+(n-1)d`, where:

• an is the nth term of the sequence,
• a1 is the first term,
• n is the term position (e.g., 1st, 5th, etc.),
• and d is the common difference.

We can find the common difference (d) by substituting -0.75 for an, -12 for a1, and 5 for n in the formula for the nth term of an arithmetic sequence:

`-0.75=-12+(5-1)d\\( -0.75=-12*4d )+12\\(11.25=4d)/4\\2.8125=d`

Thus, the common difference is 2.8125.

Writing the arithmetic sequence:

Therefore, an = -12 + (n - 1) * 2.8125 is the equation for an arithmetic sequence where -12 is the first term and -0.75 is the fifth term.