In which situation below would you want to use the Explicit Formula instead of the Recursive Formula? A. Find the 4th term when the first term is 7 and the common difference is -2.
B. Find the 7th term when the first term is -1 and the common difference is 10.
C. Find the 106th term when the first term is 2 and the common difference is 5.
D. Find the 11th term when the first term is -3 and the common difference is 4.

9514 1404 393

  all of them, possibly excepting the 4th term

Step-by-step explanation:

The recursive formula is good if you have terms near the one of interest. It might be used for the 4th term, but that would require that you compute the three previous terms:

  7, 5, 3, 1 . . . . requires 3 subtractions

It can be about as easy to calculate ...

  a4 = 7 -2(3) = 1 . . . . requires two* subtractions and a multiplication

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However, for the 7th, 11th, and 106th terms, it is impractical to list all previous terms. The explicit formula is a better choice.

A.  a4 = 7 -2(3) = 1

B.  a7 = -1 +10(6) = 59

C.  a106 = 2 +5(105) = 527

D.  a11 = -3 +4(10) = 37

* The explicit formula is ...

  an = a1 +d(n -1)

The operations identified in this formula (in the order required by the Order of Operations) are subtraction, multiplication, and addition. For a negative common difference, that amounts to two subtractions and a multiplication.

For manual evaluation, the work involved in using the recursive or explicit formulas for the 4th term is about the same, if the arithmetic is easily done mentally (as here).

question: how many people can she serve?

answer: she can serve 16.66666667 people. so she can only give 16 people a complete serving.

question: does she have enough ice cream for her guests?

answer: no. explanation: she only has enough for 16 people to have a full serving. however, she can give a 17th person a partial serving.

10.416 meters per second

step-by-step explanation:

distance=1 00 meters

time= 9.6 seconds in decimal form or 9 3/5 as a mixed number

average speed= 100/9.6

=10.416 meters per second or 10 52/125 as a mixed number.