Please solve this step by step/show your work.

Mathematics

2 answers:

const2013 [10]3 years ago

8 0

Step-by-step explanation:

m - 6 = - 3

send - 6 to the other side

m = - 3 + 6

when you send something to the other side it gets the opposite sign. If it was a minus sign it will be plus sign or if it was a minus sign it will be a plus sign. So - 6 became +6 when we send it to right side of the equation.

Now we need to sum - 3 +6

m = - 3 +6

m = + 3

You may not need the plus sign and you can directly write m = 3

Hope it was clear and it helps! Please let me know if you have any questions.

Zina [86]3 years ago

3 0

Answer:

m=9

Step-by-step explanation:

m - 6 = 3. simply add 6 to both sides to cancel

+6 +6. out the negative 6 because what

m = 9. you do on one side do on the other

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Evaluate each finite series for the specified number of terms. 1+2+4+...;n=5

zaharov [31]

Answer:

Step-by-step explanation:

The series are given as geometric series because these terms have common ratio and not common difference.

Our common ratio is 2 because:

1*2 = 2

2*2 = 4

The summation formula for geometric series (r ≠ 1) is:

$\displaystyle \large{S_n=\frac{a_1(r^n-1)}{r-1}}$ or $\displaystyle \large{S_n=\frac{a_1(1-r^n)}{1-r}}$

You may use either one of these formulas but I’ll use the first formula.

We are also given that n = 5, meaning we are adding up 5 terms in the series, substitute n = 5 in along with r = 2 and first term = 1.

$\displaystyle \large{S_5=\frac{1(2^5-1)}{2-1}}\\\displaystyle \large{S_5=\frac{2^5-1}{1}}\\\displaystyle \large{S_5=2^5-1}\\\displaystyle \large{S_5=32-1}\\\displaystyle \large{S_5=31}$

Therefore, the solution is 31.

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Summary

If the sequence has common ratio then the sequence or series is classified as geometric sequence/series.

Common Ratio can be found by either multiplying terms with common ratio to get the exact next sequence which can be expressed as $\displaystyle \large{a_{n-1} \cdot r = a_n}$ meaning “previous term times ratio = next term” or you can also get the next term to divide with previous term which can be expressed as: