-  -54 is the 14th term in the series

To find the number of terms in the series 11, 6, 1,..., -54, we need to determine the common difference (d) and the nth term of the sequence (tn) first. Then, we can use the formula to find the number of terms (n) in the sequence.

• Common difference (d):

The common difference is the difference between any two consecutive terms in an arithmetic sequence. To find the common difference, we can subtract any two consecutive terms:

d = 6 - 11 = -5 = 1 - 6 = -54 - (-5) = -49

The common difference is -5.

• nth term of the sequence (tn):

The nth term of an arithmetic sequence can be found using the formula:

tn = a + (n-1)d

where a is the first term of the sequence and d is the common difference.

In this sequence, a = 11 and d = -5. Thus, the nth term of the sequence is:

tn = 11 + (n-1)(-5) = 11 - 5n + 5 = 16 - 5n

• Number of terms (n):

To find the number of terms in the sequence, we need to determine the value of n such that tn = -54. Substituting tn and solving for n:

16 - 5n = -54

-5n = -70

n = 14

Therefore, there are 14 terms in the sequence.

Answer: Option C (14)

To summarize:

• The common difference is -5.
• The nth term of the sequence is tn = 16 - 5n.
• The number of terms is 14, as tn = -54 when n = 14.

If you think the solution is wrong then please provide your own solution below in the comments section .