Consider the sequence: 7, 64, 121, 178, 235, ... where u, = 7
a.
State whether it is arithmetic or geometric. Show how you know.

It is an arithmetic sequence.

Step-by-step explanation:

64 - 7 = 57

121 - 64 = 57

178 - 121 = 57

We have a common difference of 57, so it is arithmetic.

The explicit formula for the nth term

= 7  +57(n - 1).

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