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lutik1710 [3]
2 years ago
8

34 less than the product of 14 and an unknown number is 78

Mathematics
2 answers:
marusya05 [52]2 years ago
8 0
The answer is 8 hope i helped you!!!!!!!!!!!!!!!!
Lubov Fominskaja [6]2 years ago
6 0
34 less than (-34) the product of (multiply) 14 (14) and an unknown (x) is (=) 78 (78)

-34+14 times x=78
14 times x=14x
14x-34=78
add 34 to both sides
14x=112
divide both sdies by 14
x=8
the number is 8
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3 years ago
Find the sum of the first 20 terms of the arithmetic sequence 4, -4, -12, -20​
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Answer:

The sum of the first 20 terms is -1440.

Step-by-step explanation:

We want to find the sum of the first 20 terms of the arithmetic sequence:

4, -4, -12, -20...

The sum of an arithmetic sequence is given by:

\displaystyle S=\frac{k}{2}(a+x_k)

Where <em>k</em> is the number of terms, <em>a</em> is the initial term, and <em>x</em>_<em>k</em> is the last term.

Since we want to find the sum of the first 20 terms, <em>k</em> = 20.

Our initial term <em>a</em> is 4.

Our last term is also the 20th term as we want the sum of the first 20 terms.

To find the 20th term, we can write an explicit formula for our sequence. The explicit formula for an arithmetic sequence is given by:

x_n=a+d(n-1)

Where <em>a</em> is the initial term, <em>d</em> is the common difference, and <em>n</em> is the <em>n</em>th term.

Our initial term is 4. From the sequence, we can see that our common difference is -8 since each subsequent term is eight less than the previous term. Therefore:

x_n=4-8(n-1)

Then the last or 20th term is:

x_{20}=4-8(20-1)=4-8(19)=-148

Therefore, the sum of the first 20 terms are:

\displaystyle\begin{aligned} S_{20}&=\frac{(20)}{2}\left((4)+(-148))\\&=10(-144) \\&= -1440\end{aligned}

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