dolliemeredithm
25.04.2021 •
Mathematics
Help me with assignment
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Ответ:
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.