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Show that the sequence (p + q)^(2), (p^...

Show that the sequence ` (p + q)^(2), (p^(2) + q^(2)), (p-q)^(2) …` is an A.P.

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To show that the sequence \( (p + q)^2, p^2 + q^2, (p - q)^2 \) is an arithmetic progression (A.P.), we need to verify that the common difference between consecutive terms is the same. ### Step-by-Step Solution: 1. **Identify the Terms**: - First term \( a_1 = (p + q)^2 \) - Second term \( a_2 = p^2 + q^2 \) - Third term \( a_3 = (p - q)^2 \) ...
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AAKASH INSTITUTE ENGLISH-SEQUENCES AND SERIES -Try Yourself
  1. Write the first five terms of the following sequences and obtain the ...

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  2. Is the sequence defined by a(n) = 3n^(2) + 2 an A.P. ?

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

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

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

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

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

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

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

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  10. about to only mathematics

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

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

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  13. 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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  14. 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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  15. 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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  16. Find the sum of all integers from 1to 1001.

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

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

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

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

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