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In an A.P. the first term is 2 and the s...

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

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To solve the problem, we need to find the 20th term of an arithmetic progression (A.P.) where the first term \( a = 2 \) and the sum of the first five terms is one fourth of the sum of the next five terms. ### Step-by-Step Solution: 1. **Identify the first term and the common difference**: - Let the first term \( a = 2 \). - Let the common difference be \( d \). ...
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RD SHARMA-ARITHMETIC PROGRESSIONS-Solved Examples And Exercises
  1. If the sum of a certain number of terms of the AP 25,22,19... is 116. ...

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  2. How many terms of the A.P. -6, -(11)/2,\ -5,... are needed to give the...

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  3. In an A.P. the first term is 2 and the sum of the first five terms is ...

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  4. If Sn=n P+(n(n-1))/2Q ,w h e r eSn denotes the sum of the first n term...

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  5. The sum of n terms of two arithmetic progressions are in the ratio 5n+...

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  6. If 2/3, k ,5/8 are in A.P., find the value of kdot

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  7. If 1/a ,1/b ,1/c are in A.P. prove that: (b+c)/a ,(c+a)/b ,(a+b)/c are...

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  8. If a,b,c are in A.P., then show that (i) a^2(b+c), b^2(c+a), c^2(a+b) ...

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  9. If a, b, c are in A.P, then show that: b+c-a , c+a-b , a+b-c are in A....

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  10. If a, b, c are in A.P, then show that: b c-a^2, c a-b^2,a b-c^2 are i...

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  11. If (b+c)/a,(c+a)/b,(a+b)/c are in A.P. show that 1/a,1/b1/c are als...

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  12. If (b+c)/a ,(c+a)/b ,(a+b)/c are in A.P., prove that : b c ,\ c a ,\ a...

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  13. If a\ (1/b+1/c),\ b(1/c+1/a),\ c(1/a+1/b) are in A.P. prove that a ,\ ...

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  14. Insert 3 arithmetic means between 3 and 19.

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  15. For what value of n ,\ dot(a^(n+1)+b^(n+1))/(a^n+b^n) is the arithmeti...

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  16. Between 1 and 31 are inserted m arithmetic mean so that the ratio of t...

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  17. if the A.M. between pth and qth terms of an A.P. be equal to the A.M. ...

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  18. Find the A.M. between: 7 and 13

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  19. Find the A.M. between: 12\ a n d-8

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  20. Find the A.M. between: (x-y)a n d\ (x+y)

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