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Given that the (p+1)th term of an A.P. is twice the (q+1)th term, prove that the (3p+1)th term is twice the (p+q+1)th term.

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ICSE-SEQUENCE AND SERIES -EXERCISE 14 (b)
  1. Write the first six terms of an A.P. in which a= 7 (1)/(2) , d= 1 ...

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  2. Write the first six terms of an A.P. in which a=x ,d = 3x +2

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  3. Write the 5th and 8th terms of an AP whose 10th term is 43 and the com...

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  4. In each of the following find the terms required. (a) The seventh term...

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  5. Find the first four terms and the eleventh term of the series whose nt...

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  6. The 5th term of an A.P. is 11 and the 9th term is 7. Find the 16th ter...

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  7. Which term of the series 5, 8, 11...... is 320 ?

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  8. The fourth term of an A.P. is ten times the first. Prove that the sixt...

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  9. The fourth term of an A.P. is equal to 3 times the first term, and the...

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  10. Which term of the progression 19, 18(1)/(5), 17 (2)/(5) ,..... is the ...

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  11. Find the value of k so that 8k +4, 6k-2, and 2k + 7 will form an A.P.

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  12. Find a, b such that 7.2, a, b, 3 are in A.P.

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  13. Determine 2nd term and 5'th term of an A.P. whose 6th term is 12 and 8...

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  14. Prove that the product of the 2nd and 3rd terms of an A.P. exceeds the...

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  15. The 2nd, 31st and last term of an A.P. are 7(3)/(4) , (1)/(2) and -6(...

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  16. If 7 times the 7th term of an A.P. is equal to 11 times its 11th term,...

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  17. Determine k so that k + 2, 4k - 6 and 3k - 2 are three consecutive ter...

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  18. The pth term of an A.P. is q and the qth term is p, show that the mth ...

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  19. Let T be the rth term of an A.P. whose first term is a and conmon diff...

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

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