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Prove that the sum of nth term from the ...

Prove that the sum of nth term from the beginning and nth term from the end of an A.P. is· constant.

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To prove that the sum of the nth term from the beginning and the nth term from the end of an Arithmetic Progression (A.P.) is constant, we can follow these steps: ### Step-by-Step Solution: 1. **Define the Arithmetic Progression (A.P.):** Let the first term of the A.P. be \( A \) and the common difference be \( D \). The terms of the A.P. can be expressed as: \[ A, A + D, A + 2D, \ldots, A + (m-1)D ...
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NAGEEN PRAKASHAN ENGLISH-SEQUENCE AND SERIES-Exercise 9B
  1. (a) The nth term of a progression is (3n + 5). Prove that this progres...

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  2. (a) Find the 10th term of the progression 1 + 3 + 5 +7+ ... (b) Find...

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  3. (a) Which term of the progression 4 + 8 + 12 + ... is 76 ? (b) Which...

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  4. (a) Find the 16th term from the end of the progression 3 + 6 + 9 + ......

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  5. (a) How many numbers of two digits are divisible by 3 ? (b) How man...

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  6. (a) Find the value of 'x if x + 1, 2x + 1 and x + 1 are in A.P. Also f...

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  7. (a) The 3rd and 19th terms of an A.P. are 13 and 77 respectively. Find...

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  8. Given that the (p+1)th term of an A.P. is twice the (q+1)th term, prov...

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  9. The 12th term of an A.P. is 14 more than the 5th term. The sum of thes...

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  10. (a) Is 303, a term of the progression 5, 10, 15, ... ? (b) Is 38, a...

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  11. Prove that the sum of nth term from the beginning and nth term from th...

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  12. In an A.P., prove that : T(m+n) + T(m-n) = 2*T(m)

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  13. (i) 10 times the 10th term and 15 times the 15th term of an A.P. are e...

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  14. Which term of the A.P. (16-6i,)(15-4i), (14-2 i), ... is a : (a) pur...

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  15. (a) Which term of the progression 10,9(1)/(3),8 (2)/(3),...is the firs...

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  16. Each of two arithmetic progressions 2, 4, 6, ... and 3, 6, 9, ... are ...

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  17. If a(1),a(2),….a(n) are in arthimatic progression, where a(i)gt0 for a...

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  18. If the numbers a , b , c , d , e form an A.P. , then find the value of...

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