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Find the number of terms common to the t...

Find the number of terms common to the two AP's 3,7,11,15.... 407 and 2, 9 ,16.......709.

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`AP_1=3,7,11,...,407`
`407=3+(n-1)4`
`404=(n-1)4`
`n-1=101`
`n=102`
`AP_2=2,9,16,...,,709`
`709=2+(m-1)7`
`707=(m-1)7`
...
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RD SHARMA-ARITHMETIC PROGRESSIONS-Solved Examples And Exercises
  1. If an A.P. is such that (a4)/(a7)=2/7, find (a6)/(a8) .

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  2. The 4th term of an A.P. is three times the first and the 7th term e...

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  3. Find the number of terms common to the two AP's 3,7,11,15.... 407 and...

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  4. Show that in an A.P. the sum of the terms equidistant from the begi...

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  5. If a1,a2,a3, b, ... ,an are an A.P. of non-zero terms, prove that 1/...

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  6. If a1,a2,a3, ,an are in A.P., where ai >0 for all i , show that 1/(sqr...

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  7. The p^(t h) term of an A.P. is a and q^(t h) term is b Prove that t...

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  8. If S1,S2, S3, Sm are the sums of n terms of m A.P. ' s whose first ter...

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  9. Let Sn be the sum of first n terms of an A.P. with non-zero common d...

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  10. If there are (2n+1) terms in A.P., then prove that the ratio of the su...

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  11. The ratio of the sum of n terms of two A.P. s is (7n+1):(4n+27) . Fin...

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  12. Show that x^2+x y+y^2,z^2+xz+x^2, y^2+y z+z^2, are consecutive terms o...

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  13. If a ,b ,c are in A.P., prove that: i.(a-c)^2=4(a-b)(b-c) ii.a^2+c^2...

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  14. Find the sum of all those integers between 100 and 800 each of which o...

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  15. If the sum of m terms of an A.P. is equal to the sum of either the nex...

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  16. Suppose xa n dy are two real numbers such that the rth mean between xa...

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  17. The sum of two numbers is (13)/6dot An even number of arithmetic means...

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  18. The digits of a positive integer, having three digits, are in A.P. and...

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  19. If x ,y ,z are in A.P. and A1 is the A.M. of x and y and A2 is the A.M...

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  20. A man repays a loan of R s .3250 by paying R s .20 in the first month ...

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