CUET UG 2025 — General Test Quantitative Reasoning

The formula for the n$^{th}$th term is $a_n = 3 + 2n$an​=3+2n.

The sum of the first 24 terms is needed.

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For the first term (n = 1):

$$a_1 = 3 + 2(1)$$a1​=3+2(1)

$$a_1 = 5$$a1​=5

For the last term (n = 24):

$$a_{24} = 3 + 2(24)$$a24​=3+2(24)

$$a_{24} = 3 + 48$$a24​=3+48

$$a_{24} = 51$$a24​=51

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Checking the pattern:

$$a_1 = 5$$a1​=5

$$a_2 = 3 + 2(2) = 7$$a2​=3+2(2)=7

$$a_3 = 3 + 2(3) = 9$$a3​=3+2(3)=9

The difference between consecutive terms is always 2, so this is an arithmetic progression.

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For an arithmetic progression, the sum of n terms is:

$$S_n = \frac{n}{2} \times (\text{First term} + \text{Last term})$$Sn​=2n​×(First term+Last term)

$$S_{24} = \frac{24}{2} \times (5 + 51)$$S24​=224​×(5+51)

$$S_{24} = 12 \times 56$$S24​=12×56

$$S_{24} = 672$$S24​=672

Therefore, the sum of 24 terms is 672.