CBSE Class 11 Sequences and Series Worksheet C

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1. In an A. P. the first term is 2 and the sum of the first five terms is one fourth of next five terms. Show that 20^th term is -112.

2. Find the sum of the sequence 7, 77, 777, ------ to n terms

3. Find the sum to n terms of the series 3x8 + 6x11+ 9x14 + - - -

4. Let the sum of n, 2n, 3n terms of an A. P. be S₁, S₂ and S₃ respectively show that S₃ = 3 (S₂ – S₁)

5. Find the sum 0.6 + 0.66 + 0.666 + ---

6. If a, b, c are in A.P, b, c, d are in G. P and 1/ c,1/d, 1/e are in A. P prove that a, c, e are in G. P.

7. If a, b, c and d are in G.P show that (a²+b²+c²) (b²+c²+d²) = (ab + bc + cd)²

8. The number of bacteria in a certain culture double every hour. If there were 30 bacteria in the culture originally, how many bacteria will be present at the end of2nd hour, 4th hour and nth hour.

9. If a and b are the roots of x²-3x+p = 0 and c, d are roots of x² – 12x + 9 = 0 where a, b, c , d from G.P, prove that (q+p): (q-p) = 17:15

10. The ratio of A M and G. M of two positive no. a and b is m : n show that a : b = (m+ √m² -√ n² ): (m- √m² -√ n² )

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