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If `a ,b ,c` are in A.P., then prove that the following are also in A.P. `a^2(b+c),b^2(c+a),c^2(a+b)`

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CENGAGE PUBLICATION-SEQUENCES AND SERIES-All Questions
  1. Find the sum of the series 1.n+2(n-1)+3(n-2)+.....n.1.

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  2. Find the sum of the series (1^3)/1+(1^3+2^3)/(1+3)+(1^3+2^3+3^3)/(1+3+...

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  3. If a ,b ,c are in A.P., then prove that the following are also in A.P....

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  4. If a ,b ,c are in A.P., then prove that the following are also in A.P....

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  5. If a ,b ,c are in A.P., then prove that the following are also in A.P....

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  6. The Fibonacci sequence is defined by 1=a1=a2 and an=a(n-1)+a(n-2,)n > ...

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  7. Consider the sequence defined by an=a n^2+b n+c dot If a1=1,a2=5,a n d...

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  8. Show that the sequence 9, 12, 15, 18, ... is an A.P. Find its 16th ...

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  9. A sequence of integers a1+a2+......+an satisfies a(n+2)=a(n+1)-an fo...

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  10. Write down the sequence whose nth term is 2^n//n and (ii) [3+(-1)^n]/...

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  11. Write the first three terms of the sequence defined by a1= 2,a(n+1)=(2...

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  12. Find the sequence of the numbers defined by an={1/n , when n is odd...

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  13. Find the sum of n terms of the sequence (an),w h e r e an=5-6n ,n in ...

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  14. Show that the sequence loga ,log(a b),log(a b^2),log(a b^3), is an A.P...

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  15. Find the sum of the following series: 1/2+1/(3^2)+1/(2^3)+1/(3^4)+1/(...

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  16. Consider two A.P.: S2:2,7,12 ,17 , 500 terms a n dS1:1,8,15 ,22 , 300 ...

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  17. If pth, qth, and rth terms of an A.P. are a ,b ,c , respectively, the...

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  18. The sum of the first four terms of an A.P. is 56. The sum of the last ...

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  19. Given two A.P. 2,5,8,11...... T(60) and 3,5,7,9,......... T(50)dot Th...

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  20. In a certain A.P., 5 times the 5th term is equal to 8 times the 8th ...

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