Question

second term of an ap is 9 and sum of 6 terms of an ap is one fourth of sum of next 6 term then find the fourth term​

Answer 1

Answer:

given a + d = 9, S₆= 1/4 (S₁₂ - S₆)

to find a₄

a + d = 9...............................................(1)

S₆ = 1/4 (S₁₂ - S₆)

4S₆ = S₁₂ - S₆

5S₆ = S₁₂...............................................(2)

S₆ = 6/2 [ 2a + 5d ] = 3 [ 2a + 5d ]

S₁₂ = 12/2 [ 2a + 11d ] = 6 [ 2a + 11d ]

5*3 [ 2a + 5d ] = 6 [ 2a + 11d ] [ from equation 2 ]

=> 30 a + 75 d = 12a + 66d

=> 30a - 12a = 66d - 75d

=> 18a = - 9 d

=> 18a + 9d = 0

=> 6a + 3d = 0 ....................................(3) [ divide both sides with 3 ]

solve equations 1 and 3

a + d = 9 ......(*6)

6a + 6d = 54

6a + 3d = 0

3d = 54

d = 18

a = -9

therefore a = -9 and d = 18

a₄ = a + 3d

=> -9 + 3(18)

=> -9 + 54

=> 45