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Find the n term and the sum to n terms o...

Find the n term and the sum to n terms of the sequence: (i) 1+5+13+29+61+.......

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The correct Answer is:
(i) `2^(n + 1) - 3; 2^(n + 2) - 4 - 3n` (ii) `n^(2) + 4n + 1; (1//6)n (n + 1) (2n + 13) + n`
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ALLEN-SEQUENCE AND PROGRESSION-Exercise S-1
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  2. In an AP of which 'a' is the Ist term, if the sum of the Ist p terms i...

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  3. The interior angles of a convex polygon form an arithmetic progression...

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  4. If a gt 0, then minimum value of a + 2a^2+ a^3 + 15+ a^(-1) + a^(-3) +...

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  5. The sequence a(1), a(2), a(3), ..... A(98) satisfies the relation a(n ...

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  6. If A(1), A(2), A(3),....A(51) are arithmetic means inserted between th...

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  7. There are n AM's between 1 & 31 such that 7th mean : (n-1)th mean= 5:9...

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  8. The first term of an arithmetic progression is 1 and the sum of the fi...

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  9. For an increasing G.P. a(1), a(2), a(3),.....a(n), " If " a(6) = 4a(4)...

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  10. In a set of four number, the first three are in GP & the last three ar...

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  11. Find three numbers a, b,c between 2 & 18 such that; O their sum is 25 ...

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  12. If the 10^(th) term of an HP is 21 and 21^(st) term of the same HP is ...

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  13. The pth term Tp, of H.P. is q(p + q) and qth term Tq, is p(p+q) when p...

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  14. The harmonic mean of two numbers is 4. Their arithmetic mean A and the...

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  15. If a, b, c, d gt 0 such that a + 2b + 3c + 4d = 50, then find themaxim...

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  16. If number of coins earned in n^(th) game is n2^(n+2)-2^n and total num...

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  17. Find the n term and the sum to n terms of the sequence: (i) 1+5+13+29+...

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  18. Sum the following series to n terms and to infinity : (i) (1)/(1.4.7...

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  19. Find the value of the sum sum(k =0)^(359) k. cos k^(@)

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