Question

Find the 7th term in thesequence-4,-8, -16, . . .

Answer 1

Answer:

The 7th term is -256

Step-by-step explanation:

Given:

-4,-8, -16, . . .

To find:

The 7th term in the sequence

We were not informed the type of sequence, we need to check if it has a common difference or common ratio

common difference (d) = next term - previous term

d = -8 - (-4) = -8 + 4 = -4

d = -16 - (-8) = -16 + 8 = -8

No common difference

Common ratio (r) = next term/previous term

r = -8/-4 = 2

r = -16/-8 = 2

The ratio is common. Hence, it is a geometric sequence

To get the 7th term, we will apply the formula:

`\begin{gathered} a_n\text{ = ar}^(n-1) \\ \\ a_n\text{ = nth term} \\ r\text{ = common ratio} \\ a\text{ = first term} \\ n\text{ = number of terms} \end{gathered}`
`\begin{gathered} a\text{ = -4, r = 2} \\ when\text{ n = 7} \\ a_7\text{ = -4 }*\text{ 2}^(7-1)\text{ } \\ \\ a_7\text{ = -4 }*\text{ 2}^6 \\ \\ a_7\text{ = -256} \end{gathered}`