In an arithmetic sequence, the 1st term is -12, the 17th term is 12 and the last term is 45. Then how many terms are there in the sequence?Question 4Answera.39b.35c.40d.45

To find the number of terms in the arithmetic sequence, we can use the formula for the nth term of an arithmetic sequence:

an = a1 + (n-1)d

where an is the nth term, a1 is the first term, n is the number of terms, and d is the common difference.

Given that the first term (a1) is -12 and the 17th term (a17) is 12, we can substitute these values into the formula:

12 = -12 + (17-1)d

Simplifying the equation, we get:

12 = -12 + 16d

Adding 12 to both sides, we have:

24 = 16d

Dividing both sides by 16, we find:

d = 24/16 = 3/2

Now, we can find the last term (an) using the formula:

an = a1 + (n-1)d

Substituting the values, we get:

45 = -12 + (n-1)(3/2)

Simplifying the equation, we have:

45 = -12 + (3/2)n - 3/2

Adding 12 to both sides and simplifying further, we get:

57 = (3/2)n

Multiplying both sides by 2/3, we find:

n = (2/3) * 57 = 38

Therefore, there are 38 terms in the arithmetic sequence.