The 4th term of an ap is three times the first and the 7th term exceeds twice the third term by 1. Find the first term and the common difference?

Answers (1)

Assume the a.p has first term "a" and common difference "d".

ATQ

a + 3d = 3a

2a = 3d ...(i)

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

2a + 4d + 1 = a + 6d 

a = 2d - 1 ...(ii)

Put value of a in equation (ii)

2 (2d -1) = 3d

4d - 3d = 2

d =2 

a = 4-1 = 3

Hence the first tem and common difference of a.p. is 3,2 respectively.

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