CUET UG 2025 — General Test Quantitative Reasoning

The 3rd term of an A.P. is 1 and the 9th term is 19.

In an Arithmetic Progression, the nth term is given by:

$$a_n = a + (n - 1)d$$an​=a+(n−1)d

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

---

For the 3rd term:

$$a_3 = a + 2d$$a3​=a+2d

$a + 2d = 1$a+2d=1 ... (Equation 1)

For the 9th term:

$$a_9 = a + 8d$$a9​=a+8d

$a + 8d = 19$a+8d=19 ... (Equation 2)

---

Subtracting Equation 1 from Equation 2:

$$(a + 8d) - (a + 2d) = 19 - 1$$(a+8d)−(a+2d)=19−1

$$6d = 18$$6d=18

$$d = 3$$d=3

---

Substituting $d = 3$d=3 into Equation 1:

$$a + 2(3) = 1$$a+2(3)=1

$$a + 6 = 1$$a+6=1

$$a = -5$$a=−5

---

The 23rd term is:

$$a_{23} = a + 22d$$a23​=a+22d

$$a_{23} = -5 + 22(3)$$a23​=−5+22(3)

$$a_{23} = -5 + 66$$a23​=−5+66

$$a_{23} = 61$$a23​=61

Therefore, the 23rd term is 61.