14. The last term of an arithmetic sequence is 207, the common difference is 3, and the number of terms is 14. What is the first term of the sequence?:

A. 165

B. 171

C. 249

D. 168

Please explain. thanks

The last term of an arithmetic sequence is 207, the common difference is 3, and the number of terms is 14. What is the first term of the sequence?:

A. 165

B. 171

C. 249

D. 168

Please explain. thanks

The last, or nth, term of an arithmetic progression is defined by L = a + (n - 1)d where L = the last term, a = the first term, n = the number of terms and d = the common difference.

Therefore, 207 = a + (14 - 1)3
...............= a + 39

Therefore, a = 207 - 3396 = 168.

Subtract the difference from the last term 13 times, since the last term is the 14th number. Can you think of a faster way to do this?

I hope this helps. Thanks for asking.

To find the first term of the arithmetic sequence, we can use the formula:

Last term (L) = First term (a) + (n - 1) * Common Difference (d)

Given:
Last term (L) = 207
Common difference (d) = 3
Number of terms (n) = 14

Substituting the given values into the formula, we get:

207 = a + (14 - 1) * 3

Simplifying the equation:

207 = a + 13 * 3

207 = a + 39

Subtracting 39 from both sides of the equation:

168 = a

Therefore, the first term of the sequence is 168.

So the answer is D. 168.

To find the first term of the arithmetic sequence, we can use the formula:

nth term (Tn) = first term (a) + (n-1) * common difference (d)

Given information:
Last term (Tn) = 207
Common difference (d) = 3
Number of terms (n) = 14

Using the formula, we can plug in the given values and solve for the first term (a):

Tn = a + (n-1) * d

207 = a + (14-1) * 3

Simplifying the equation:

207 = a + 13 * 3
207 = a + 39

Subtracting 39 from both sides:

207 - 39 = a
168 = a

Therefore, the first term of the arithmetic sequence is 168.

So, the answer is option D.