Q #1

⏰ :

Second term of a GP is 1000 and the common ratio is r = 1/n where n is a natural number. P_{n} is the product of n terms of this GP. P_{6} > P_{5} and P_{6} > P_{7}, what is the sum of all possible values of n?

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Q #2

⏰ :

Sum of first 12 terms of a GP is equal to the sum of the first 14 terms in the same GP. Sum of the first 17 terms is 92, what is the third term in the GP?

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Q #3

⏰ :

Sum of first 25 terms in AP is 525, sum of the next 25 terms is 725, what is the common difference?

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Q #4

⏰ :

Let the n^{th} term of AP be defined as t_{n}, and sum up to 'n' terms be defined as S_{n}. If |t_{8}| = |t_{16}| and t_{3} is not equal to t_{7}, what is S_{23}?

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Q #5

⏰ :

a, b, c, d and e are 5 distinct numbers that from an arithmetic progression. They are not necessarily consecutive terms but form the first 5 terms of the AP. It is known that c is the arithmetic mean of a and b, and d is the arithmetic mean of b anc c. Which of the following statements are true?

i. Average of all 5 terms put together is c.

ii. Average of d and e is not greater than average of a and b.

iii. Average of b and c is greater than average of a and d.

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