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Determine the number of terms in the A.P. 3,4,5, …, 399 . Also find its ` 25^(th)` term .

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To solve the problem, we need to determine the number of terms in the arithmetic progression (A.P.) given by 3, 4, 5, ..., 399, and also find the 25th term of this A.P. ### Step-by-Step Solution: 1. **Identify the First Term (a) and Common Difference (d)**: - The first term \( a = 3 \). - The second term is \( 4 \), so the common difference \( d = 4 - 3 = 1 \). ...
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AAKASH INSTITUTE ENGLISH-SEQUENCES AND SERIES -Try Yourself
  1. Is the sequence defined by a(n) = 3n^(2) + 2 an A.P. ?

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  2. Show that the sequence (p + q)^(2), (p^(2) + q^(2)), (p-q)^(2) … is a...

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  3. Determine the number of terms in the A.P. 3,4,5, …, 399 . Also find ...

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  4. Find the indiated terms in each of the following A.P. (i) 1, 7, 1...

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  5. The 11^(th) of an A.P. is 80 and the 16^(th) term is 110 . Find the...

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  6. In an A.P., the p^(th) term is 1/q and the q^(th) term is 1/p. fin...

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  7. The sum of three numbers in A.P. is 27 and the sum of their squares i...

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  8. 4. (a) Divide 20 into 4 parts which are in A.P. and such that the prod...

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  9. about to only mathematics

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  10. If a ,b ,c are in A.P., prove that the following are also in A.P. (i) ...

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  11. If a^(2), b^(2),c^(2) are in A.P prove that (a)/(b+c), (b)/(c+a) ,(c)...

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  12. If (b-c)^2,(c-a)^2,(a-b)^2 are in A.P. prove that 1/(b-c),1/(c-a),1/(a...

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  13. If a,b,c are in A.P. prove that: a(1/b+1/c),b(1/c+1/a),c(1/a+1/b) are ...

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  14. If a^2(b+c),b^2(c+a),c^2(a+b), are in A.P. show that either a ,b ,c ar...

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  15. Find the sum of all integers from 1to 1001.

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  16. Solve: 1+4+7+10+...+x=590.

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  17. How many term of the A.P. 15 , 12, 9 ., - are needed to give the sum ...

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  18. Let S1, S2 and S3 be the sum of n terms of 3 arithmetic series, the fi...

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  19. If the sum of n tems of a series be 5n^2+3n, find its nth term. Are th...

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  20. The ratio of the sum of n terms of two A.P.\'s is (3n+1):(4n+3). Find ...

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