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The sum of n terms of two arithmetic pro...

The sum of `n` terms of two arithmetic progressions are in the ratio `5n+4:9n+6.` Find the ratio of their 18th terms.

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To solve the problem step by step, we will use the properties of arithmetic progressions (AP) and the formula for the sum of the first n terms of an AP. ### Step-by-Step Solution: 1. **Understand the Problem**: We are given that the sum of the first n terms of two arithmetic progressions (AP1 and AP2) is in the ratio \(5n + 4 : 9n + 6\). We need to find the ratio of their 18th terms. 2. **Formula for Sum of n Terms**: The sum of the first n terms of an arithmetic progression is given by the formula: \[ ...
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RD SHARMA ENGLISH-ARITHMETIC PROGRESSIONS-All Questions
  1. In an A.P. the first term is 2 and the sum of the first five terms is ...

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

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

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  5. 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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  6. 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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  7. If a, b, c are in A.P, then show that: b+c-a ,\ c+a-b ,\ a+b-c are in ...

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

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  9. 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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  10. 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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  11. 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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  12. Insert 3 arithmetic means between 3 and 19.

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

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

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

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

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

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

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  19. Insert 4 A.M.s between 4 and 19.

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  20. Insert 7 A.M.s between 2 and 17.

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