#### 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.