Create an explicit equation for the recursively-defined sequence below. **Optional table** to help convert the recursive equation to explicit: 4=15; +1=3• t(n) 1 t(n) = Submit 3

Q: Find the sixth term of a geometric sequence whose second term is 3 and whose fourth term is 1/3.…

A: Now dividing equation (2) by equation (1), we get Therefore sixth term is,

Q: Find the recursive and explicit formula for each arithmetic sequence. Explicit formulas need to be…

A:

Q: Determine whether sequence having the given nth term is monotonic           an = 3 + (−1)n

A: an = 3 + (−1)n We need to determine whether the sequence having the nth term is monotonic or not.

Q: Find an explicit formula for the general term an of the sequence. {1,- -/-/- 3 5

A:

Q: Find the 4th term in the sequence with the following definition:

A:

Q: The first eight terms of a sequence are as follows: 2, 6, 12, 20, 30, 42, 56, 72, Find a closed…

A:

Q: The sequence with general term an = (-1)" is divergent. True False

A: The given sequence is divergent.

Q: Find the first five terms of the recursively defined infinite sequence.

A:

Q: Find the nth term an of a sequence whose first four terms are given. 2, 4, 8, 16,....

A:

Q: Write the first five terms of the sequence: 13 In n n n=1 Determine whether the sequence converges,…

A: Given that: 13lnnnn=1∞

Q: Find the infinite sum of the geometric sequence with a1 = 3, r = if it exists. 8

A:

Q: Write a rule for the n th term of the geometric sequence for which a, = 64 and a,=1.

A: Solving by geometric sequence we have

Q: Find the partial sum S, of the geometric sequence that satisfies the given conditions. az = 36, ag =…

A: Let we have a geometric series with first term a and common ratio r then the formula for the nth…

Q: Write a rule for the n th term of the sequence for which a =3 andr Identify the first six terms of…

A:

Q: Calculate the first 5 terms of the sequence an = Factions and as decimals to 3dp. (1+)", expressing…

A:

Q: What are the initial term and a recursive formula for this sequence: 4, 7, 10, 13, ......

A: The given sequence is 4,7,10,13,... the common difference is 7-4=3,10-7=3,... therefore, the common…

Q: 2 if it exists. 6 Find the infinite sum of the geometric sequence with a = 3, r = Preview

A: Given  a = 3  r = 2/6

Q: What is the 7th term of the geometric sequence defined by the rulean = -3(2)^n-1 ?

A: What is the 7th term of the geometric sequence

Q: Find the infinite sum of the geometric sequence with 2 if it exists. 7 a = 4, r = -

A:

Q: Consider the geometric sequence whose nth term is __. This sequence can also be defined recursively…

A: We need a sequence here.

Q: What is the 11th term of the geometric sequence −1.5, −3, −6, −12, ...

A:

Q: Give an example of a single sequence that meets all the following criteria, or explain why this is…

A: This is not possible.   Result : every bounded below and decreasing sequence of real numbers are…

Q: What are the first five terms of the sequence defined over the natural numbers with the explicit…

A:

Q: Create an explicit equation for the recursively-defined sequence below. **Optional table** to help…

A:

Q: write the first five terms of the sequence defined recursively. a, = 15, akti =(-3)aK %3D KtI

A: Given a1=15 and ak+1=-3(ak)So the first 5 terms of the sequence will be a1,a2,a3,a4,a5

Q: Find n such that the geometric sequence becomes less than 1: {400, 240, 144, 86.4, ...} n3D

A:

Q: aj = -1 and an V(- 2an-1)² + 1 for n > 2

A:

Q: Find the infinite sum of the geometric sequence with 2 if it exists. 8 6, г a = -

A: The geometric sequence with a=6, r=28

Q: Find ag from a geometric sequence where the first term is 63 and r is 0.4. Round to 4 decimal…

A:

Q: Find the first four terms of the sequence defined by а, — 3 %3D а, 3 За, —1 + 2, for all n > 1

A:

Q: What are the first 5 terms of the sequence represented by а %3D 2n - За 'n – 1, where ", =4,

A:

Q: Determine the sum of the first 6 terms of the geometric sequence. 1,2, 4, .. So

A: A geometric progression is a type of sequenc in which ratio of two consecutive terms is always a…

Q: Which arithmetic sequence has a first term equal to 47 and a common difference of -18?

A: To find the arithmetic sequence

Q: What will be the sum of first 6 terms of he geometric sequence with the first term a1=2 and a2=24

A:

Q: What is a recursively defined sequence?

A:

Q: Choose an expression for the apparent nth term of the sequence. Assume that n begins with 1. 1,-1,…

A: Given sequence 1 , -1  , 1 , -1 ,  1 ,  . . . . . .

Q: how that the sequence (1 – (-1)" +1/n) is divergen

A:

Q: Find an explicit formula for a sequence of the form     with the initial terms given below. 4, 8,…

A: Given sequence 4, 8, 16, 32, 64, 128, 256....... here  84=168=3216=..........=2 i.e. they have a…

Q: Create your own sequence with recursive formula.

A:

Q: List the first five terms of the sequence defined by An = (-1)".10"-1 %3D

A: SOLUTION-

Q: Write Hhe first 3 terns For this recursively defined sequence

A: The solution is in step 2

Q: Find the infinite sum of the geometric sequence with 3 if it exists. a = 2, r =

A:

Q: Find an explicit formula for the sequence 1/2,-1/3,1/4,-1/6....

A:

Q: Find the sum to the nearest tenth of the first 17 terms of the sequence defined by the recursion a…

A: Given first term ( a ) = 5 Next term of series = 1.1 + an-1 This defines an A.P. with first term of…

Q: An arithmetic sequence has a first term of 0 and a 9th term of 12. Which term number corresponds to…

A:

Q: (2п)! An

A:

Q: Find the fifth term in the sequence that is defined as follows: an = 4 + (-1)" Enter

A:

Q: Find the nth term of a sequence whose first several terms are given. 7, 2, –3, –8, ... an

A:

Q: Find the infinite sum of the geometric sequence with a = 6, r = if it exists. %3D %3D

A:

Q: Find the indicated nth partial sum of the arithmetic sequence. 6.3, 6.1, 5.9, 5.7,. . .,   n = 13

A: Given arithmetic sequence is  6.3, 6.1, 5.9, 5.7,...... we are given with arithmetic sequence, so…

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.