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If the third term of a G.P. is the square of the first and the fifth term is 64 the series would be __________.
- a)4+8+16+32+…
- b)4-8+16-32+…
- c)Both
- d)None
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
If the third term of a G.P. is the square of the first and the fifth t...
The general form of a G.P. is a, ar, ar^2, ar^3, ....
Let the first term be a.
Then, the third term is ar^2 and it is given that ar^2 = a^2.
Solving this, we get r = a.
Therefore, the G.P. is a, a^2, a^3, a^4, a^5.
Given, the fifth term is 64.
So, a^5 = 64.
Solving this, we get a = 2.
Therefore, the G.P. is 2, 4, 8, 16, 32.
Let the first term be a.
Then, the third term is ar^2 and it is given that ar^2 = a^2.
Solving this, we get r = a.
Therefore, the G.P. is a, a^2, a^3, a^4, a^5.
Given, the fifth term is 64.
So, a^5 = 64.
Solving this, we get a = 2.
Therefore, the G.P. is 2, 4, 8, 16, 32.
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If the third term of a G.P. is the square of the first and the fifth term is 64 the series would be __________.a)4+8+16+32+…b)4-8+16-32+…c)Bothd)NoneCorrect answer is option 'C'. Can you explain this answer?
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