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

Question

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

anonymous · Answer

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

mathmale · Answer

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?