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The ratio of the sum of n terms of two A...

The ratio of the sum of `n` terms of two A.Ps is `(7n+1):(4n+27)dot` Find the ratio of their `m^(t h)` terms.

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To find the ratio of the m-th terms of two arithmetic progressions (APs) given the ratio of their sums of n terms, we can follow these steps: ### Step 1: Understand the Sum of n Terms of an AP The sum of the first n terms of an AP can be expressed as: \[ S_n = \frac{n}{2} \times [2a + (n-1)d] \] where \( a \) is the first term and \( d \) is the common difference. ### Step 2: Set Up the Given Ratio ...
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RD SHARMA-ARITHMETIC PROGRESSIONS-All Questions
  1. In a school students thought of planting trees in and around the sc...

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  2. The sum of the first p , q , r terms of an A.P. are a , b , c respecti...

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  3. The ratio of the sum of n terms of two A.Ps is (7n+1):(4n+27)dot Find ...

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  4. If there are (2n+1) terms in A.P., then prove that the ratio of the s...

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  5. Raghav buys a shop of Rs. 1,20,000. He pays half of the amount in cash...

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  6. Which term of the A.P. 3,15,27, 39, ... will be 120 more than its 21st...

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  7. The 17th term of an A.P. is 5 more than twice its 8th term. If the ...

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  8. The sum of three numbers in A.P. is -3, and their product is 8. Find t...

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  9. Find the four numbers in A.P. whose sum is 20 and the sum of whose ...

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  10. The sum of three terms of an A.P. is 21 and the product of the first ...

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  11. The angles of a quadrilateral are in A.P. whose common difference is 1...

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  12. Consider the A.P. 2,5,8, 11 ,........ ,302. Show that twice of the mi...

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  13. For what value of n the n^(t h) terms of the following two A.Ps the s...

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  14. How many terms are there in the sequence 3,6,9, 12 , 111 ?

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  15. Find the middle term of the A.P. 6, 13 , 20 , ...... 216.

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

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  17. Which term of the sequence -1,3,7, 11 , 95 ?

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  18. Write the sequence with nth terms: an=3+4n (ii) an=5+2n an=6-n (iv) a...

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  19. Then n^(t h) term of an A.P. is 6n+2. Find the common difference.

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  20. Show that the sequence defined by an=5n-7 is an A.P., find its common...

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