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Gala2k [10]
2 years ago
10

What is the sum of the first 10 terms of the sequence defined by an=3n-3?

Mathematics
2 answers:
igomit [66]2 years ago
4 0

Answer:

The sum of first 10 terms of the sequence defined by a_n=3n-3 is 135.

Step-by-step explanation:

Given : nth term of a sequence as a_n=3n-3

We have to find the sum of first 10 terms of the sequence.

Consider the nth term of a sequence as a_n=3n-3

Then put n = 1  to get the first term

a_1=3(1)-3=0

put n = 2 to get the next term

a_2=3(2)-3=6-3=3

put n = 3 to get the next term

a_3=3(3)-3=9-3=6

put n = 4 to get the next term

a_4=3(4)-3=12-3=9

Thus, the sequence is of the form 0, 3, 6, 9,.....

Thus, the above is an arithmetic sequence with a = 0 and common difference (d) = 3

Thus, Sum of 10 terms is given by

S_n=\frac{n}{2}(2a+(n-1)d)

n = 10 , a = 0 , d = 3

Put we get,

S_{10}=\frac{10}{2}(2(0)+(10-1)3)

Simplify, we have,

S_{10}=5(9\times 3)

S_{10}=135

Thus, the sum of first 10 terms of the sequence defined by a_n=3n-3 is 135.

netineya [11]2 years ago
3 0
The answer is D. 135
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The volume of the oblique cone is 144.49 cubic inches , if an oblique cone has a radius of 4 units, a height of 8.5 units, and a slant length of 11.7 inches.

Step-by-step explanation:

             An oblique cone has a radius of 4 units

             A height of 8.5 units

             A slant length of 11.7 inches

We have to use the slant height to calculate actual base

So in a right angle triangle when two sides are given the third side is calculated by

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Formula to calculate the volume of oblique cone,......................(1)

V = \frac{1}{3} bh

If r is the distance of the base of the height from the center of the circle [ this is because the base of the height is outside the oblique cone]

V = \frac{1}{3} \pi r^{2} h

Where r is the distance if the base of the height from the center of the circle [ this is because the base of the height is outside the oblique cone]

Here r = 8.03 - 4 = 4.03 units

Volume = \frac{1}{3}× 3.14 × 4.03 × 4.03 × 8.5

Volume = 144.49 cubic inches

Hence, the volume of the oblique cone is 144.49 cubic inches , if an oblique cone has a radius of 4 units, a height of 8.5 units, and a slant length of 11.7 inches.

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Read 2 more answers
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