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Find the n th term and the sum of first ...

Find the n th term and the sum of first n terms of thefollowing sequence `2,7,20,57,166,..`

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The correct Answer is:
n th term `=2*3^(n-1)+n-1 and "sum" =3^(n)+(n(n-1))/(2)-1`
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CHHAYA PUBLICATION-MISCELLANEOUS EXAMPLES-ALGEBRA
  1. Show that the following two A.P. is have 14 common terms 3,7,11,15...,...

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  2. Show that there are 17 identical terms in the following two A.P. 2,5,8...

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  3. Find the n th term and the sum of first n terms of thefollowing sequen...

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  4. Solve |x^(2)+4x+3|+2x+5=0

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  5. For a gt0, determine all the roots of the equations x^(2)-2a|x-a|-3a...

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  6. How many five -digit numbers divisible by 3 can do formed using the d...

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  7. How many five-digit telephone numbers with pairwise distinct digits ca...

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  8. Five speakers A,B,C,D and E will speark at a meeting. In how many ways...

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  9. If z(1)=3i and z(2)=-1-i , where i=sqrt(-1) find the value of arg ((z(...

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  10. Show that the number of solutions of equations |x|^(2)-3|x|+2=0 is 4.

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  11. Show that (1)/(2)[(x-y)^(4)+(y-z)^(4)+(z-x)^(4)] is perfect square.

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  12. In an arithmetic progression of n terms ( n is even) , the two middle ...

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  13. In an A.P. fo n terms (n is even), the two middle terms are (alpha- be...

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  14. Prove that the ineuations (2x+1)/(7x-1) gt 5 and (x+7)/(x-8)gt2 have n...

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  15. If the argument of (z-a)(barz-b) is equal to that of ((sqrt(3)+i)(1+sq...

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  16. Which term of the series 3+4+6+9+13+18+.. is 5053?

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  17. z(1) and z(2)( ne z(1)) are two complex numbers such that |z(1)|=|z(2...

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  18. If x= cos theta+ I sin theta and y= cos psi + I sin psi, then show tha...

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  19. If omegais an imaginary cube root of unity, show that (x+omega+ omeg...

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  20. If omegais an imaginary cube root of unity, show that (a+ bomega+com...

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