Question

Can anyone pls help me in math?

Answer 1

-22, -28

`\displaystyle \large{a_n=-6n+2}`

Explanation:

Given:

• Sequence -4, -10, -16, __, __

Since the sequence doesn’t have common ratio, find common difference by subtracting the next term with previous term:

-10-(-4) = -10+4 = -6

-16-(-10):= -16+10 = -6

Therefore, there is a common difference which is -6. Hence, this sequence is arithmetic sequence.

To find next term, add the term with common difference:

-16-6 = -22

-22-6 = -28

Therefore, the finished sequence is -4, -10, -16, -22, -28

Next, find the rule which is the general term (nth term) for this sequence. The formula/rule is:

`\displaystyle \large{a_n=a_1+(n-1)d}`

Where
`\displaystyle \large{a_n}` is nth term,
`\displaystyle \large{a_1}` is first term and
`\displaystyle \large{d}` is common difference. We know that first term is -4 and common difference is -6. Hence:

`\displaystyle \large{a_n=-4+(n-1)(-6)}\\\\\displaystyle \large{a_n=-4-6n+6}\\\\\displaystyle \large{a_n=-6n+2}`

Thus, the rule is
`\displaystyle \large{a_n=-6n+2}`