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If a, b, c are in A.P., prove that a^(2)...

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

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` :. a^(2)(b+c),b^(2)(c+a),c^(2)(a+b)` are in A.P
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MTG IIT JEE FOUNDATION-ARITHMETIC PROGRESSIONS -SOLVED EXAMPLES
  1. If seven times the seventh term of an A.P is equal to eleven times it...

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  2. If ( a^(n+1) + b^(n+1)) / (a^n +b^n) is the AM between a and b. Then ...

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  3. In a flower bed, there are 23 rose plants in the first row, 21 in the ...

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  4. Find the sum of first 24 terms of the list of numbers whose nth term ...

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  5. The p^(t h),q^(t h)and r^(t h)terms of an A.P. are a, b, c, respectiv...

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  6. In an A.P., the sum of first n terms is (3n^2)/2+(5n)/2dot Find its 25...

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  7. If a,b,c are in AP show that (i) 1/(bc) ,1/(ca),1/(ab) are in AP....

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  8. If a, b, c are in A.P., prove that a^(2)(b+c),b^(2)(c+a),c^(2)(a+b)" a...

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  9. Find a(1),a(2),a(3) if the n^(th) term is given by a(n)=(n-1)(n-2)(3+n...

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  10. Find a(3),a(5),a(8) if the n^(th) term is given by a(n)=(-1)^(n)n

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  11. If the n^(th) term of the A.P. 9, 7, 5, .... is same as the n^(th) ter...

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  12. The 7t h term of an A.P. is 32 and its 13 t h term is 62. Find t...

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  13. Find the term of the arithmetic progression 9,12,15,18, ... which is 3...

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  14. The sum of three numbers in A.P. is 12 and the sum of their cubes is ...

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  15. Find the value of x for which (8x+4),\ (6x-2) and (2x+7) are in A.P...

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  16. Find the sum of all integers between 0 and 500 which are divisible by ...

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  17. If the sum of 7 terms of an A.P. is 49 and that of 17 terms is 289,...

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  18. The first term of an A.P is 7 , the last term is 47 and the sum is 432...

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  19. A man is employed to count Rs. 10710. He counts at the rate of Rs. 180...

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  20. In an A.P., the first term is 22, n t h term is -11 and the sum ...

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