A certain arithmetic sequence has this explicit formula for the nth term: an = 12 + (n - 1)(5)
The same sequence has this recursive formula:
an = an-1
+
What number belongs in the blank space in the recursive formula?
A. 5
B. 12
о
C. 17
D. 4

A. 5

Step-by-step explanation:

I assume the definitions are

an = 12 + (n-1)×5

an = an-1 + blank

if this is correct, then we have

a1 = 12

a2 = 12 + 5 = 17 = a1 + 5

a3 = 12 + 2×5 = 22 = a2 + 5

a4 = 12 + 3×5 = 27 = a3 + 5

...

we see, for an we need to add (n-1) times the number 5 to the initial a1 value.

so every new sequence number is larger by 5 than the previous one.

hence the answer.

correct answer is b. 27/8

step-by-step explanation:

x =-.20752

step-by-step explanation:

4^(x+2)=12

4^(x+2)=12

take the log base 4 on each side

log 4 (4^(x+2) = log 4(12)

we know log b(a^y) = y log b (a)

(x+2) log 4(4) = log 4 (12)

x+2 = log 4 (12)

we know   logb c = loga c/loga b

we want to convert to base 10   so a = 10

by default, we do not write the 10   c = 4   and b = 10

log4 10 = log 12/log 4

log4 10 = log 12/ log 4

x+2 = log 12/ log 4

subtract 2 from each side

x +2 -2 = log 12/ log 4 -2

x = 1.79248125 -2

x =-.20752