Quantitative Reasoning

Progression & Series

Medium

In an arithmetic progression, if 6 is the third term, the ninth term exceeds the seventh term by 3, then 12 is which term?

Fifth

Ninth

Seventh

Eighth

✅ Correct Option: 3

In an arithmetic progression, the 3rd term is 6 and the 9th term exceeds the 7th term by 3.

The general formula for the nth term of an arithmetic progression is:

nth term $= a + (n-1)d$

where $a$ is the first term and $d$ is the common difference.

The 9th term is 2 positions away from the 7th term.

9th term - 7th term $= 2d$

$2d = 3$

$d = 1.5$

The 3rd term is 6:

$a + (3-1)d = 6$

$a + 2d = 6$

$a + 2(1.5) = 6$

$a + 3 = 6$

$a = 3$

To find which term is 12:

$a + (n-1)d = 12$

$3 + (n-1)(1.5) = 12$

$(n-1)(1.5) = 9$

$n-1 = 6$

$n = 7$

Therefore, 12 is the 7th term of the arithmetic progression.

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In an arithmetic progression, if 6 is the third term, the ninth term exceeds the seventh term by 3, then 12 is which term?

Solution

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