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A sprial is made up of successive semici...

A sprial is made up of successive semicircles, with centres alternately at A and B, starting with centre at A, of radii 0.5 cm, 1.0 cm, 1.5 cm , 2.0 cm, ….. As shown in figure. What is the total length of such a spiral made up of thirteen consecutive semicircles? (Take `pi = 22/7`)
[Hint : Length of successive semicircles is `l_(1), l_(2), l_(3), l_(4),`...... with centres at A, B,A,B, ....., respectively.]

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VGS PUBLICATION-BRILLIANT-PROGRESSIONS-Exercise 6.3
  1. Find the sums given below: (iii) -5+(-8)+(-11)+……+(-230)

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  2. In an AP: (i) Given a = 5, d = 3, a(n) = 50, find n and S(n).

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  3. In an AP: (ii) Given a = 7, a(13) = 35, find d and S(13).

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  4. In an AP: (iii) Given a(12) = 37, d = 3, find a and S(12).

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  5. In an AP: (iv) Given a(3) = 15, S(10) = 125, find d and a(10).

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  6. In an AP: (v) Given a = 2, d = 8, S(n) = 90, find n and a(n).

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  7. In an AP: (vi) Given a(n) = 4, d = 2, S(n) = -14, find n and a.

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  8. In an AP: (vii) Given l = 28, S = 144, and there are total 9 terms. ...

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  9. The first and the last terms of an A.P. are 17 and 350 respectively. I...

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  10. Find the sum of first 51 terms of an AP whose second and third terms a...

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  11. If the sum of first 7 terms of an AP is 49 and that of 17 terms is 289...

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  12. Show that a(1), a(2), …….., a(n)….. form an AP where a(n) is defined a...

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  13. Show that a(1), a(2),……, a(n)…. Form an AP where a(n) is defined as be...

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  14. If the sum of the first n terms of an AP is 4n-n^(2) , what is the fir...

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  15. Find the sum of the first 40 positive intergers divisible by 6.

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  16. A sum of Rs. 700 is to be used to give seven cash prizes to students ...

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  17. In a school, students thought of planting trees in an around the schoo...

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  18. A sprial is made up of successive semicircles, with centres alternatel...

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  19. 200 logs are stacked in the following manner : 20 logs in the bottom r...

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  20. In a bucket and ball race, a bucket is placed at the starting point. W...

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