CUET UG 2025 — General Test Quantitative Reasoning

The series is: $4 + 6 + 8 + \ldots + 196$4+6+8+…+196

Here, $196$196 is the last term of the series (not the sum).

This is an Arithmetic Progression (AP) where:

First term $(a) = 4$(a)=4

Common difference $(d) = 6 - 4 = 2$(d)=6−4=2

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Using the $n$nth term formula of an AP:

$$a_n = a + (n - 1)d$$an​=a+(n−1)d

Where $a_n = 196$an​=196, $a = 4$a=4, $d = 2$d=2:

$$196 = 4 + (n - 1) \times 2$$196=4+(n−1)×2

$$192 = (n - 1) \times 2$$192=(n−1)×2

$$96 = n - 1$$96=n−1

$$n = 97$$n=97

There are $97$97 terms in total.

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Since $97$97 is odd, there is exactly one middle term. For any odd number of terms, the middle term is at the position that has an equal number of terms on both sides of it:

$$\text{Middle position} = \dfrac{n + 1}{2}$$Middle position=2n+1​

$$= \dfrac{97 + 1}{2}$$=297+1​

$$= \dfrac{98}{2}$$=298​

$$= 49$$=49

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Using the $n$nth term formula:

$$a_{49} = 4 + (49 - 1) \times 2$$a49​=4+(49−1)×2

$$= 4 + 96$$=4+96

$$= 100$$=100

Therefore, the middle term of the series is $100$100.