4th term of an AP

Algebra Level 2

If the 8 8 th term of an arithmetic progression is twice its 6 6 th term, what is the 4 4 th term of the arithmetic progression?


The answer is 0.

Srinivasa Gopal by Srinivasa Gopal , 53, India

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2 solutions

Srinivasa Gopal
Mar 7, 2020

Let the initial term and the common difference of the AP be "a" and "d" respectively. Eighth term of an AP is a + 7d and its sixth term is a + 5d

a + 7d = 2*(a+5d) = 2a + 10d

a = - 3d -----(1)

Fourth term = a + 3d = 0 from (1)

2 Helpful 0 Interesting 0 Brilliant 0 Confused

a 8 = 2 ( a 6 ) a_8 = 2(a_6)

a 1 + 7 d = 2 ( a 1 + 5 d ) a_1 + 7d = 2(a_1 + 5d)

a 1 + 7 d = 2 a 1 + 10 d a_1 + 7d = 2a_1 + 10d

a 1 = − 3 d a_1 = -3d

a 4 = a 1 + 3 d = − 3 d + 3 d = 0 a_4 = a_1 + 3d = -3d + 3d = \boxed{0}

1 Helpful 0 Interesting 0 Brilliant 0 Confused

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