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If S(n) be the sum of n consecutive term...

If `S_(n)` be the sum of n consecutive terms of an A.P. show that,
`S_(n+3) - 3S_(n+2) + 3S_(n+1) - S_(n) = 0`

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CHHAYA PUBLICATION-SEQUENCE AND SERIES-Exercise 9 B (Long Answer Type Questions)
  1. The first and last terms of an A.P. are a and l respectively. If S be ...

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  2. If the first, second and last terms of A.P. be a, b, and c respectivel...

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  3. If S(n) be the sum of n consecutive terms of an A.P. show that, S(n+...

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  4. If S(n) be the sum of n consecutive terms of an A.P. show that, S(n+...

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  5. Let a(n) denote the n-th term of an A.P. and p and q be two positive i...

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  6. Find the sum of the three-digited natural numbers which leave a remain...

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  7. Between the roots of the quadratic equation 3px^(2) - 10px + 5q = 0 (p...

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  8. Let a(n) be the nth term of an A.P. and a(3) + a(5) + a(8) + a(14) + a...

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  9. Find the sum upto the nth term of the series (1+3) + (5+7+9+11) + (13 ...

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  10. If S(1), S(2), S(3) are the sums of n natural numbers, their squares, ...

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  11. If a(1) = 2 and a(n) - a(n-1) = 2n (n ge 2), find the value of a(1) + ...

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  12. Find the middle term of the series 1+5+9+…+101.

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  13. If (b^(2) + c^(2) - a^(2))/(2bc), (c^(2) + a^(2) - b^(2))/(2ca), (a^(2...

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  14. To verify the cash balance, the auditor of Jaya Bank Ltd. Employs his ...

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  15. A polygon has 25 sides, the lengths of which starting from the smalles...

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  16. A sets out from a certain place and tavels 1 mile the first day, mile...

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  17. A man arranges to pay off a debt of Rs. 12000 in 30 annual instalments...

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  18. A man divides Rs. 24000 among his four sons in such a way that the amo...

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  19. Two posts are offered to a man. In the first one, the starting salary ...

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  20. The salary of a man starts at Rs. 800 and increases annually by Rs. 20...

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