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4th Term of an A.P is Equal to 3 Times Its First Term and 7th Term Exceeds Twice the 3rd Time by I. Find the First Term and the Common Difference. - ICSE Class 10 - Mathematics

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Question

4th term of an A.P is equal to 3 times its first term and 7th term exceeds twice the 3rd time by I. Find the first term and the common difference.

Solution

The general term of an AP is given by `t_n = a + (n - 1)d`

Now `t_4 = 3 xx a`

=> a + 3d = 3a

=> 2a - 3d = 0 ...(1)
Next `t_7 - 2 xx t_3 =1`

=> a + 6d - 2(a + 2d) = 1

=> a + 6d -2a - 4d = 1

=> -a + 2d = 1 .....(ii)
multiplying (ii) by 2 we get

-2a + 4d = 2 ....(iii)

Adding equation (i) and (iii) we get

d = 2

Substituting the value of d in (ii) we get

`-a + 2 xx 2 = 1`

`=> -a + 4 = 1`

=> a = 3

Hence a = 3 and d = 2

  Is there an error in this question or solution?
Solution 4th Term of an A.P is Equal to 3 Times Its First Term and 7th Term Exceeds Twice the 3rd Time by I. Find the First Term and the Common Difference. Concept: Arithmetic Progression - Finding Their General Term.
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