Question

The common difference of an arithmetic sequence is -5 . If a_(12) is 22, what is a_(1) ?

Answer 1

The first term of the arithmetic sequence is 77.

Step-by-step explanation:

An arithmetic sequence is a sequence of numbers in which the difference between any two consecutive terms is constant. In this case, the common difference is given as -5.

To find the value of a1, we can use the formula for the nth term of an arithmetic sequence: an = a1 + (n-1)d, where a1 is the first term, d is the common difference, and n is the term number.

1. Given that a12 = 22, we can substitute the values into the formula: 22 = a1 + (12-1)(-5)
2. Simplifying the equation, we get 22 = a1 + 11(-5)
3. Further simplifying, we have 22 = a1 - 55
4. Adding 55 to both sides of the equation, we get 77 = a1

Therefore, the first term of the arithmetic sequence, a1, is 77.