Question

Find n for the arithmefic sequence in which a_(n)=32,a_(1)=-12, and d=2

Answer 1

In an arithmetic sequence with the first term of -12 and a common difference of 2, the value of n for which the n-th term is 32 is n = 23.

Step-by-step explanation:

To find the value of n for the arithmetic sequence where an = 32, a1 = -12, and the common difference d = 2, we can use the formula for the n-th term of an arithmetic sequence:

an = a1 + (n - 1)d

Plugging in the given values, we get:

32 = -12 + (n - 1)(2)

To solve for n, first add 12 to both sides:

44 = (n - 1)(2)

Now, divide both sides by 2:

22 = n - 1

Finally, add 1 to both sides to isolate n:

n = 23

Therefore, the value of n is 23.