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The 4th term of an A.P. is three times t...

The 4th term of an A.P. is three times the first and the 7th term exceeds twice the third term by four. Find the first term and the common difference.

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Let the A.P be -`a,a+d,a+2d............`
according to the question,`a+3d=3a`...(1) and `a+6d=2(a+2d)+4`....(2)
From (1) and(2) `d=8 `and `a=12`
the A.P is `12,20,28,36,44........`
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RD SHARMA-ARITHMETIC PROGRESSIONS-Solved Examples And Exercises
  1. If a1,a2,a3, ,an are in A.P. with common difference d(w h e r ed!=0), ...

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  2. If an A.P. is such that (a4)/(a7)=2/7, find (a6)/(a8) .

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

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

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

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

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

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

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

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  13. 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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  14. 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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  15. Find the sum of all those integers between 100 and 800 each of which o...

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

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

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

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  20. 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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