Question

In an arithmetic sequence, the ratio of the first term to the second is 2 : 3. What is the ratio of the third term to the fifth term?

Answer 1

Let the first and the second term of the arithmetic sequence be 2x and 3x respectively.

⇒ a + b = 2x … (1)

Also, 2a + b = 3x

⇒ a + a + b = 3x

⇒ a + 2x = 3x (From equation (1))

⇒ a = 3x − 2x = x

Putting the value of a in equation (1):

x + b = 2x

⇒ b = 2x − x = x

Third term of the given arithmetic sequence = 3a + b = 3x + x = 4x

Fifth term of the given arithmetic sequence = 5a + b = 5x + x = 6x

Ratio of the third term to the fifth term =