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Volgvan
3 years ago
7

Use inductive reasoning to find the next term in this sequence 2,3,5,9,17. Then explain the rule for the pattern.

Mathematics
1 answer:
NISA [10]3 years ago
7 0

We have been given the sequence 2,3,5,9,17.

We can write the terms of this sequence as

2=2^0+1\\
3=2^1+1\\
5=2^2+1\\
9=2^3+1\\
17=2^4+1\\

From the above term we can see that for the first term we take exponent 0 on 2 and then add 1 .

For second term we take exponent 1 on 2 and then add 1 .

For third term we take exponent 2 on 2 and then add 1 .

Using this fact for the next term of the sequence i.e. 6th term, we can take exponent 5 on 2 and then add 1 .

Therefore, next term of the sequence is given by

2^5+1\\
=32+1\\
=33

Therefore, the next term is 33.

Using the above facts, the pattern is given by

a_n=2^{n-1}+1

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Answer:

Answer on Question #47534 – Math – Geometry

How to prove the volume formula of con is 1/3×π×r^2×h;without using

integration?

Solution.

Suppose we take a slice of the pyramid with the cone inside, from some way up

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The area of the square is × =

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of the area

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So the cone's volume is

∗

=

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