MATH SOLVE

6 months ago

Q:
# Which answer is the explicit rule for the sequence 12.5, 11, 9.5, 8, 6.5, 5 ... ?

Accepted Solution

A:

Answer:[tex]a_n = 14-1.5n[/tex]Step-by-step explanation:The explicit rule for the arithmetic sequence is given by:[tex]a_n =a_1+(n-1)d[/tex] ....[1]where,[tex]a_1[/tex] is the first termd is the common difference and n is the number of terms.Given sequence: 12.5, 11, 9.5, 8, 6.5, 5 ...This is an arithmetic sequence.here, [tex]a_1=12.5[/tex] and d =- 1.5Substitute these in [1] we have;[tex]a_n = 12.5+(n-1)(-1.5)[/tex]⇒[tex]a_n = 12.5-1.5n+1.5[/tex]⇒[tex]a_n = 14-1.5n[/tex]Therefore, the explicit rule for the given sequence is, [tex]a_n = 14-1.5n[/tex]