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Can anyone pls help me in math?

Can anyone pls help me in math?-example-1
User Ajmicek
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Answer:

-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}

User Wik
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