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ivanzaharov [21]
3 years ago
6

The first term of an arithmetic sequence is −12 . The common difference of the sequence is 7. What is the sum of the first 30 te

rms of the sequence? Enter your answer in the box.
Mathematics
1 answer:
Olenka [21]3 years ago
8 0

Answer:

2685

Step-by-step explanation:

The nth term of an arithmetic sequence is:

aₙ = a₁ + d (n − 1)

where a₁ is the first term and d is the common difference.

Here, a₁ = -12 and d = 7:

aₙ = -12 + 7 (n − 1)

aₙ = -12 + 7n − 7

aₙ = -19 + 7n

The sum of the first n terms of an arithmetic sequence is:

S = (n/2) (a₁ + aₙ)

First, we find the 30th term:

a₃₀ = -19 + 7(30)

a₃₀ = 191

Now we find the sum:

S = (30/2) (-12 + 191)

S = 2685

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A line with a slope (m) and a point (a, b) is represented in point-slope form as, y - b = m(x - a).

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Negative reciprocal of 1 is -1.

The slope of the line would be m = -1.

Substitute m = -1 and (a, b) = (2, 5) into y - b = m(x - a) to wrote the equation:

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5 0
2 years ago
A box is 12 centimeters wide ,12 centimeters long, and 15 centimeters tall. What is the total surface area of 4 such boxes?
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First you want to find the surface area of one box
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━━━━━━━━━━━━━━━ ♡ ━━━━━━━━━━━━━━━  

A multiple is a number that can be divided by that number with no remainder. For example, multiples of 5 are 5, 10, 15, and 20.

A multiple of 12 is basically 12 × (number of multiple), for example, if you want the second multiple of 12, you would multiply 2 by 12.

So multiply 12 by 1, 2, 3, 4, and 5.

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12×3=36

12×4=48

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The first five multiples of 12 are 12, 24, 36, 48, and 60.

━━━━━━━━━━━━━━━ ♡ ━━━━━━━━━━━━━━━  

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Answer:

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