CUET UG 2025 — General Test Quantitative Reasoning

For any term in an arithmetic progression:

$n$nth term $= a + (n - 1)d$=a+(n−1)d

Where $a$a is the first term, $d$d is the common difference, and $n$n is the position of the term.

---

Given that the 5th term is 7:

$$a + (5 - 1)d = 7$$a+(5−1)d=7

$a + 4d = 7$a+4d=7 -----(Equation 1)

---

Given that the 9th term is 13:

$$a + (9 - 1)d = 13$$a+(9−1)d=13

$a + 8d = 13$a+8d=13 -----(Equation 2)

---

Subtracting Equation 1 from Equation 2:

$$(a + 8d) - (a + 4d) = 13 - 7$$(a+8d)−(a+4d)=13−7

$$a + 8d - a - 4d = 6$$a+8d−a−4d=6

$$4d = 6$$4d=6

$$d = \dfrac{6}{4}$$d=46​

$$d = 1.5$$d=1.5

---

Substituting $d = 1.5$d=1.5 into Equation 1:

$$a + 4(1.5) = 7$$a+4(1.5)=7

$$a + 6 = 7$$a+6=7

$$a = 1$$a=1

---

The 15th term is:

$$a + (15 - 1)d$$a+(15−1)d

$$= 1 + 14(1.5)$$=1+14(1.5)

$$= 1 + 21$$=1+21

$$= 22$$=22

Therefore, the 15th term is 22.