Consider the sequence: 8, 11, 14, 17, 20, 23, 26, ... Write a recursive definition.
1 answer:
The first term is 8, so
Each time we want a new term, we add on 3
8+3 = 11
11+3 = 14
14+3 = 17
17+3 = 20
23+3 = 26
and so on
This recursive step of adding on 3 to the prior term is written as this: which says "to get the nth term, add 3 to the term just before the nth term"
Based on what you posted for your answer choices, the final answer is likely choice C. However it seems some weird typo happened.
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Answer:
(a) -7 , - 9 , - 11
(b) Arithmetic sequence
(c) There is a common difference of -2
(d) -53
Step-by-step explanation:
(a) To find the next three terms , we must firs check if it is arithmetic sequence or a geometric sequence . For it to be an arithmetic sequence , there must be a common difference :
check :
-3 - (-1) = -5 - (-3) = -7 - (-5) = -2
This means that there is a common difference of -2 , which means it is an arithmetic sequence.
The next 3 terms we are to find are: 5th term , 6th term and 7th term.
= a + 4d
= - 1 + 4 ( -2 )
= -1 - 8
= - 9
6th term = a +5d
= -1 + 5(-2)
= -1 - 10
= - 11
= a + 6d
= -1 + 6 (-2)
= -1 - 12
= -13
Therefore : the next 3 terms are : -9 , -11 , - 13
(b) it is an arithmetic sequence because there is a common difference which is -2
(c) Because of the existence of common difference
(d) = a + 26d
= -1 + 26 ( -2 )
= -1 - 52
= - 53