What are the explicit equation and domain for a geometric sequence with a first term of 4 and a second term of −12? an = 4(−3)n − 1; all integers where n ≥ 1 an = 4(−3)n − 1; all integers where n ≥ 0 an = 4(36)n − 1; all integers where n ≥ 1 an = 4(36)n − 1; all integers where n ≥ 0

; all integers where n ≥ 1

Step-by-step explanation:

We are given that the first term of the sequence is 4 i.e. and second term is -12 i.e. .

Now, the nth term of geometric sequence is given by,

, where r is the common ratio of the sequence.

So, using the given values we get,

i.e.

i.e.

i.e. r = -3.

Now the explicit formula for the geometric equation is given by,

.

i.e. , where

Hence option first is correct.

= 5

step-by-step explanation:

to find the 15th term substitute n = 15 into the nth term formula

= (- 3 × 15 ) + 50 = - 45 + 50 = 5