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The first and last terms of an A.P. are ...

The first and last terms of an A.P. are a and l respectively. If S be the sum of the terms then show that the common difference is `(l^(2) - a^(2))/(2S - (l+a))`.

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CHHAYA PUBLICATION-SEQUENCE AND SERIES-Exercise 9 B (Long Answer Type Questions)
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  4. If the first, second and last terms of A.P. be a, b, and c respectivel...

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

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

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

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

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

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

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

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

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

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