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If a(n)=3-4n, then show that a(1),a(2),a...

If `a_(n)=3-4n`, then show that `a_(1),a_(2),a_(3), …` form an AP. Also, find `S_(20)`.

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To solve the problem, we need to show that the sequence defined by the nth term \( a_n = 3 - 4n \) forms an arithmetic progression (AP) and then find the sum of the first 20 terms of this sequence. ### Step 1: Find the first few terms of the sequence We will calculate the first four terms of the sequence: 1. **First term \( a_1 \)**: \[ a_1 = 3 - 4 \cdot 1 = 3 - 4 = -1 ...
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NCERT EXEMPLAR ENGLISH-ARITHMETIC PROGRESSIONS-Short Answer Type Questions
  1. Find the 12th term from the end of the AP -2, -4, -6, …, -100.

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  2. Which term of the AP 53, 48, 43, … is the first negative term ?

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  3. How many numbers lie between 10 and 300, which divided by 4 leave a re...

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  4. Find the sum of two middle terms of the AP -4/3,-1,-2/3,-1/3,...,4(1/3...

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  5. The first term of an AP is -5 and the last term is 45. If the sum of t...

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  6. Find the sum (i) 1+(-2)+(-5)+(-8)+ … +(-236) (ii) (4-(1)/(n))+(4-(...

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  7. Which term of the AP -2,-7,-12, … will be -77 ? Find the sum of this A...

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  8. If a(n)=3-4n, then show that a(1),a(2),a(3), … form an AP. Also, find ...

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  9. In an AP, If S(n)=n(4n+1), then find the AP.

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  10. In an AP, If S(n)=3n^(2)+5n and a(k)=164, then find the value of k.

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  11. If S(n) denotes the sum of first n terms of an AP, then prove that S(1...

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  12. Find the sum of first 17 terms of an AP whose 4th and 9th terms are -1...

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  13. If sum of first 6 terms of an AP is 36 and that of the first 16 terms ...

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  14. Find the sum of all the 11 terms of an AP whose middle most term is 30...

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  15. Find the sum of last ten terms of the AP 8, 10, 12, …, 126.

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  16. Find the sum of first seven numbers which are multiples of 2 as well a...

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  17. How many terms of the AP -15, -13, -11, … are needed to make the sum ...

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  18. The sum of the first n terms of an AP whose first term is 8 and the co...

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  19. Kanika was given her pocket money on Jan 1st , 2008. She puts Rs. 1 on...

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  20. Yasmeen saves Rs. 32 during the first month, Rs. 36 in the second mont...

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