CUET PG 2023 — Reasoning PYQ

Pattern Analysis

By observing the terms, we can see that each term follows the general formula:

Let's verify this for each known term:

• For $n=1$:

  $$3^1+1=3+1=4$$

• For $n=2$:

  $$3^2+1=9+1=10$$

• For $n=4$:

  $$3^4+1=81+1=82$$

• For $n=5$:

  $$3^5+1=243+1=244$$

• For $n=6$:

  $$3^6+1=729+1=730$$

Alternative Pattern (Recursive)

Alternatively, we can observe that each term is multiplied by $3$ and then $2$ is subtracted:

Verification:

• $$(4\times 3)-2=12-2=10$$
• $$(82\times 3)-2=246-2=244$$
• $$(244\times 3)-2=732-2=730$$

Calculating the Missing Term

Using either pattern, we can find the missing term ($n=3$):

Using the power formula:

Using the recursive formula:

To confirm, check if the next term follows:

Final Answer

The missing term in the series is $28$.