Q19 of 40 Page 1

If the first three terms of an A.P are b, c and 2b, then find the ratio of b and c.

2 : 3


Given – b, c and 2b are in A.P.


To Find – ratio b:c


Properties –


If a, b, c are in A.P., then (b – a) = (c – b), that is the difference between two consecutive terms of an A.P. is same.


Answer –


As the terms b, c & 2b are in A.P., we can write


∴ c – b = 2b – c


∴ c + c = 2b + b


∴ 2c = 3b



∴ b : c = 2 : 3


Therefore, the ratio of b and c is 2:3.


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