Find the first three terms of the A.P. whose first term is 2/3 and common difference is 1/3?

1/3, 1, 4/3, 5/3, .......

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1/3, -1, 4/3, 5/3, .......

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-1/3, 1, 4/3, 5/3, .......

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5/3, 4/3, 1, .......

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Solution

The correct option is B 1/3, 1, 4/3, 5/3, .......
Let the series be $a_{1}, a_{2}, a_{3}, a_{4}, . . . . . .$
$a_{1} = a = 2 / 3$
Common difference = 1/3
$a_{2} = a_{1} + d = 2 / 3 + 1 / 3 = 1$
$a_{3} = a_{2} + d = 1 + 1 / 3 = 4 / 3$
$a_{4} = a_{3} + d = 4 / 3 + 1 / 3 = 5 / 3$
Therefore, first three terms of this A.P. will be 1/3, 1,4/3, 5/3, ......

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