Consider the following sequence 152, -76, 38, -19
Write a rule for the nth term and then find

a₇ =  2.375

Step-by-step explanation:

There is a common ratio r between consecutive terms, that is

r = = = = -

This indicates the sequence is geometric with nth term

= a₁

where a₁ is the first term and r the common ratio

Here a₁ = 152 and r = - , then

= 152 , so

a₇ = 152 = 152 × = 2.375

for this case we must apply distributive property to the following expression:

the distributive property states that:

then, when applying the property we have to multiply the -2 for each term within the parenthesis: