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xenn [34]
3 years ago
8

What is the number of the terms of geometrical sequence if its first, fourth and the last term is equal to 2, 54 and 486 respect

ively.
Mathematics
1 answer:
slega [8]3 years ago
3 0

Answer:

The number of terms of the G.P. is 6

Step-by-step explanation:

Let the G.P. has first term a, common ratio r and the number of terms n.

The G.P. has first term 2, so a = 2.

Now, the fourth term is 54 i.e. ar³ = 54

⇒ 2r³ = 54

⇒ r³ = 27

⇒ r = 3

Now, the last term i.e. the nth term is= ar^{n - 1} = 486

⇒ 2 \times 3^{n - 1} = 486

⇒ 3^{n - 1} = 243 = 3^{5}

Hence, (n - 1) = 5

⇒ n = 6

So the number of terms of the G.P. is 6 (Answer)

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Step-by-step explanation:

Let label the Triangles first,

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Solution:

In right triangle  By Pythagoras Theorem,

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In right triangle Δ ADB andΔ ADC  By Pythagoras Theorem we will have,

AB² =  BD² + AD²

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and

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Now in right triangle Δ ABC,

BC² = AB² + AC²

Equating equation  (1 ) and ( 2 ) and the given value we get

52² = 50² + x² + 2² + x²

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