Question

The seventh term of ap is 4 times its 2nd term aand the 12th term is 2 more than 3 times of its 4th term.find the progression

Answer 1

Step-by-step explanation:

Given

seventh term (a7) = 4 times its second term (a2)

i.e.

a+6d = 4 (a+d)

a+6d = 4a+4d

2d = 3a

d= 3a/ 2...... (i)

It is also given that

a12 = 3 (a4) +2

a+11d = 3(a+3d) +2

a+11d = 3a+ 9d + 2

a + 11 (3a/2) = 3a + 9 (3a /2) + 2

a+ 33a/2 = 3a + 27a/2 + 2

(2a+33a/2) = (6a + 27a + 4/2 )

Cancel 2 on both sides,

35a = 33a + 4

35a - 33a = 4

2a = 4

a = 2

d= 3a/2

d = 6/2 = 3

the A.P is 2, 5, 8, 11......