Question

-17/4 is the __________ term of 2 ¼, 2, 1 ¾.

Answer 1

\[a_{1} = 2 \frac{ 1 }{ 4 }(6)\]?

Answer 2

Notice that each term (except for the last) is 1/4 less than the previous term. For example, If the first term is 2 1/4. the second is 2 1/4 - 1/4 = 2.

There's a formula for arithmetic sequences:

l = a + (n-1)d,

where l = the last term;
a = the first term, and
n = the number of terms.

What are l, a and n in this problem? Given this formula, and these values of l, a and n, can you now solve for n, the number of terms?

If all else fails, you could just keep writing out terms of this sequence until you reach -17/4.

9/4, 8/4, 7/4, .... , -15/4,-16/4, -17/4. How many terms do you then have?