Kate jogged for 37 minutes, 23 seconds, and Phil jogged for 23 minutes, and 43 seconds. (a) How much longer did Kate jog than
Phil? (b) What was the combined jogging time for the two?
(1 min. = 60 sec.)

a. 13 min, 40 sec

b. 81 min, 6 sec

Step-by-step explanation:

 The correct options are

Part A : option (a) the common difference is -10.

Part B : option (c) 3,  -2,  -7,  -12,  .   .   .

Step-by-step explanation:  We are given to solve the following two problems

PART A :  

We are given to select the statement that best describes the relationship between the successive terms in the following sequence :

9,   -1,   -11,    -21,   .   .   .

If a(n) denotes the n-th term of the given sequence, then we see that

Since the difference between any two consecutive term of the given sequence is -10, so

there is a common difference of -10.

Option (a) is CORRECT.

PART B :  

Given that a sequence is defined recursively using th efollowing formula :

We are to select the sequence that could be generated using formula (i).

Let f(n) = 1. Substituting n = 1, 2, 3, 4,  .  .  . in equation (i), we get

In this case, the sequence is 1, -4, -9, -14,  .  .  .

Let f(n) = 2. Substituting n = 1, 2, 3, 4,  .  .  . in equation (i), we get

In this case, the sequence is 2, -3, -8, -13,  .   .   .

Let f(n) = 3. Substituting n = 1, 2, 3, 4,  .  .  . in equation (i), we get

In this case, the sequence is 3, -2, -7, -12,  .   .   .

Let f(n) = 4. Substituting n = 1, 2, 3, 4,  .  .  . in equation (i), we get

In this case, the sequence is 4,-1, -6, -11,  .   .   .

Thus, the correct sequence that could be generated is 3, -2, -7, -12,  .  .  .

Option (c) is CORRECT.