CUET UG 2025 — General Test Quantitative Reasoning

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 $= a + (n-1)d$=a+(n−1)d

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

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

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

$$2d = 3$$2d=3

$$d = 1.5$$d=1.5

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The 3rd term is 6:

$$a + (3-1)d = 6$$a+(3−1)d=6

$$a + 2d = 6$$a+2d=6

$$a + 2(1.5) = 6$$a+2(1.5)=6

$$a + 3 = 6$$a+3=6

$$a = 3$$a=3

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To find which term is 12:

$$a + (n-1)d = 12$$a+(n−1)d=12

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

$$(n-1)(1.5) = 9$$(n−1)(1.5)=9

$$n-1 = 6$$n−1=6

$$n = 7$$n=7

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