The recursive forula of an arithmetic sequence is described below. a1=19,an−1+6 Which represent the explicit of this aritmetic sequence? A. an=6n+13 B. an=6n+19 C. an=13n+6 D. an=19n+6

Question

The recursive forula of an arithmetic sequence is described below.    a1=19,an−1+6    Which represent the explicit of this aritmetic sequence?    A. an=6n+13    B. an=6n+19    C. an=13n+6    D. an=19n+6

Oung1985 · Accepted Answer

Given,     a1=19,an=an−1+6    Here first term is 19 and each next term is obtained by adding 6 to its previous term.    That is,    a1=19    d=6    Step 2    Now explicit equation is,    an=a1+(n—1)    ⇒an=19+(n−1)⋅6    ⇒an=19+6n−6    ⇒an=6n+13

Jeffrey Jordon · Accepted Answer

Answer is given below (on video)

xleb123 · Accepted Answer

Answer:B.&amp;nbsp;an=6n+19}Explanation:The recursive formula of an arithmetic sequence is given as a1=19, an=an−1+6. To find the explicit formula of this arithmetic sequence, we need to express an in terms of n without reference to previous terms.Let&#039;s analyze the recursive formula. We notice that each term is obtained by adding 6 to the previous term. Since the common difference in an arithmetic sequence remains constant, we can determine the explicit formula by considering the initial term and the common difference.Let&#039;s determine the explicit formula step by step:- We start with the given initial term a1=19.- The common difference is the value added to each term to obtain the next term. In this case, the common difference is 6.- To express the n-th term an, we can observe that the number of common differences between a1 and an is (n−1), as we have (n−1) steps from the first term to the n-th term.- Therefore, we can express the explicit formula as an=a1+(n−1)·common&amp;nbsp;difference.Substituting the values we have:an=19+(n−1)·6.Now, let&#039;s determine the explicit form of the arithmetic sequence using the given options:A. an=6n+13B. an=6n+19C. an=13n+6D. an=19n+6We can see that the correct option is B.&amp;nbsp;an=6n+19, as it matches the explicit formula we derived.

Jazz Frenia · Accepted Answer

Given recursive formula: an=an−1+6To find the explicit formula, we need to express an in terms of n.To do this, we&#039;ll substitute an−1 in the recursive formula with the explicit formula an−1=6(n−1)+13:an=(6(n−1)+13)+6Simplifying, we have:an=6n−6+13+6an=6n+13Hence, the explicit formula for the arithmetic sequence is an=6n+13.Therefore, the correct option is A.an=6n+13.

Andre BalkonE · Accepted Answer

The recursive formula of an arithmetic sequence is given by an=an−1+6, where a1=19. We need to find the explicit formula for this arithmetic sequence.To find the explicit formula, we can start by examining the pattern in the sequence.For the first term, we are given that a1=19.For the second term, we have a2=a1+6=19+6=25.For the third term, we have a3=a2+6=25+6=31.We can observe that each term is obtained by adding 6 to the previous term.Based on this pattern, we can infer that the explicit formula for this arithmetic sequence is of the form an=an+b, where a is the common difference and b is the initial term.To find the values of a and b, we can consider the first two terms of the sequence:Using the given information, we have:a1=19a2=19+6Since the common difference is 6, we can write:a2=a1+6Substituting the values of a1 and a2, we get:19+6=19+6Simplifying, we have:25=25This equation is true, which confirms that the common difference is indeed 6.Therefore, the explicit formula for the arithmetic sequence is:an=6n+bTo find the value of b, we can substitute the value of a1 into the explicit formula:19=6(1)+bSimplifying, we have:19=6+bSubtracting 6 from both sides, we get:13=bTherefore, the explicit formula for the arithmetic sequence is:an=6n+13

The recursive forula of an arithmetic sequence is described below. NS

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