What is the recursive formula for this geometric sequence?–4, –24, –144, –864, ...A.{𝑎1=−6𝑎𝑛=𝑎𝑛−1∙4{ a 1 =−6a n =a n−1 ∙4 B.{𝑎1=−4𝑎𝑛=𝑎𝑛−1∙6{ a 1 =−4a n =a n−1 ∙6 C.{𝑎1=−4𝑎𝑛=𝑎𝑛−1∙30{ a 1 =−4a n =a n−1 ∙30 D.{𝑎1=−6𝑎𝑛=𝑎𝑛−1∙30{ a 1 =−6a n =a n−1 ∙30
Question
What is the recursive formula for this geometric sequence?–4, –24, –144, –864, ...A.{𝑎1=−6𝑎𝑛=𝑎𝑛−1∙4{ a 1 =−6a n =a n−1 ∙4 B.{𝑎1=−4𝑎𝑛=𝑎𝑛−1∙6{ a 1 =−4a n =a n−1 ∙6 C.{𝑎1=−4𝑎𝑛=𝑎𝑛−1∙30{ a 1 =−4a n =a n−1 ∙30 D.{𝑎1=−6𝑎𝑛=𝑎𝑛−1∙30{ a 1 =−6a n =a n−1 ∙30
Solution
The recursive formula for a geometric sequence is given by a_n = a_n-1 * r, where r is the common ratio.
To find the common ratio, we divide any term by the previous term.
For example, -24 / -4 = 6, -144 / -24 = 6, -864 / -144 = 6.
So, the common ratio (r) is 6.
The first term (a_1) of the sequence is -4.
Therefore, the recursive formula for this geometric sequence is {a_1 = -4, a_n = a_n-1 * 6}.
So, the correct answer is B. {a_1 = -4, a_n = a_n-1 * 6}.
Similar Questions
What is the recursive formula for this arithmetic sequence?–7, –1, 5, 11, ...A.{𝑎1=−7𝑎𝑛=𝑎𝑛−1−6{ a 1 =−7a n =a n−1 −6 B.{𝑎1=11𝑎𝑛=𝑎𝑛−1−6{ a 1 =11a n =a n−1 −6 C.{𝑎1=11𝑎𝑛=𝑎𝑛−1+6{ a 1 =11a n =a n−1 +6 D.{𝑎1=−7𝑎𝑛=𝑎𝑛−1+6{ a 1 =−7a n =a n−1 +6 SUBMITarrow_backPREVIOUS
Which of the following recursive formulas represents the same geometric sequence as the formula an = 2 • 3(n – 1)?A.{𝑎1=3𝑎𝑛=𝑎𝑛−1∙2{ a 1 =3a n =a n−1 ∙2 B.{𝑎1=3𝑎𝑛=𝑎𝑛−1+2{ a 1 =3a n =a n−1 +2 C.{𝑎1=2𝑎𝑛=𝑎𝑛−1∙3{ a 1 =2a n =a n−1 ∙3 D.{𝑎1=2𝑎𝑛=𝑎𝑛−1∙6{ a 1 =2a n =a n−1 ∙6 SUBMITarrow_backPREVIOUS
Which recursive formula can be used to represent the sequence 2, 4, 6, 8, 10, ... ?A.𝑎1=0𝑎𝑛=𝑎𝑛−1+2 a 1 =0a n =a n−1 +2 B.𝑎1=2𝑎𝑛=𝑎𝑛−1∙2 a 1 =2a n =a n−1 ∙2 C.𝑎1=2𝑎𝑛=𝑎𝑛−1+2 a 1 =2a n =a n−1 +2 D.𝑎1=2𝑎𝑛=𝑎𝑛−1−2 a 1 =2a n =a n−1 −2 SUBMITarrow_backPREVIOUS
Instructions: Given the recursive rule, match it to the explicit form.Recursive: an=an−1+9𝑎𝑛=𝑎𝑛−1+9a1=13𝑎1=13Drag answer hereRecursive: an=an−1+4𝑎𝑛=𝑎𝑛−1+4a1=−22𝑎1=−22Drag answer hereRecursive: an=an−1−9𝑎𝑛=𝑎𝑛−1−9a1=3𝑎1=3Drag answer hereRecursive: an=an−1+20𝑎𝑛=𝑎𝑛−1+20a1=−38𝑎1=−38Drag answer hereExplicit: an=12−9n𝑎𝑛=12−9𝑛Explicit: an=4+9n𝑎𝑛=4+9𝑛Explicit: an=−26+4n𝑎𝑛=−26+4𝑛Explicit: an=−58+20n𝑎𝑛=−58+20𝑛
A certain arithmetic sequence has this explicit formula for the nth term:an = 13 + (n – 1)(6)The same sequence has this recursive formula:an = an–1 + ________What number belongs in the blank space in the recursive formula?A.19B.5C.13D.6SUBMITarrow_backPREVIOUS
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.