Question

Given that −6, − 2 1
2
, . . . , 71 is a linear
sequence, Calculate the number of terms in the
sequence.
A. 21
B. 22
C. 23
D. 24

Answer 1

To find the number of terms in a linear sequence, we need to first find the common difference (d) between consecutive terms. We can do this by subtracting the second term from the first term:

d = (-21/2) - (-6) = (-21/2) + 12/2 = -9/2

Now we can find the number of terms (n) in the sequence using the formula:

a_n = a_1 + (n-1)d

where a_1 is the first term, a_n is the last term, and d is the common difference.

We know that a_1 = -6 and a_n = 71, so we can substitute these values into the formula along with d = -9/2:

71 = -6 + (n-1)(-9/2)

Multiplying both sides by -2/9 gives:

-142/9 = -12 + (n-1)

Adding 12 to both sides gives:

102/9 = n-1

Simplifying gives:

n = 121/9

This is not a whole number, so we need to round up to the nearest integer since the sequence contains a finite number of terms. Therefore, the number of terms is:

n = 14

But we need to add one more term to include the second term (-21/2) that we left out when calculating the common difference. Therefore, the total number of terms in the sequence is:

n = 14 + 1 = 15

Answer: There are 15 terms in the sequence, which is not one of the options given in the answer choices. Therefore, this question may contain an error.