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navik [9.2K]
3 years ago
14

How many terms are there in a geometric series if the first term is 3, the common ratio is 4 and the sum of the series is 1,023

Mathematics
1 answer:
Olenka [21]3 years ago
4 0
The sum of a geometric sequence is:

s(n)=a(1-r^n)/(1-r) in our case:

s(n)=3(1-4^n)/(1-4)

s(n)=-(1-4^n)

s(n)=(4^n)-1  and s=1023

(4^n)-1=1023

4^n=1024

n ln4=ln1024

n=(ln1024)/(ln4)

n=5
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The statements that are true about the pyramid are

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<h3>Properties of a Square pyramid </h3>

From the question, we are to determine the statements that are true about the pyramid

The diagram shows a square pyramid,

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and

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Since the pyramid is a square pyramid,

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Since the height of a triangular face is 612 ft,

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Thus, the second statement is true

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All four triangular faces are congruent

∴ The fourth statement is true

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The pyramid has four lateral faces which are each a triangle

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Hence, the statements that are true about the pyramid are

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Learn more on Pyramid here: brainly.com/question/10042135

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