CAT To find the nth term of an AP MCQ - Practice Questions & Answers

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4 Questions around this concept.

Concepts Covered - 1

To find the nth term of an AP

Formula to find the nth term of an AP:

$\mathrm{a_n = a + (n-1) \times d}$

Where:

$\mathrm{- a_n}$ is the nth term

- a is the first term

- d is the common difference

- n is the number of terms

Foundation Building Questions:

Question 1: The 5th term of an AP is 16 and the 8th term is 25. Find the nth term of this AP.

Solution:

Using $\mathrm{a_n = a + (n-1) \times d}$

For $\mathrm{n=5, a_5 = a + 4d = 16}$

For $\mathrm{n=8, a_8 = a + 7d = 25}$

From these equations, we get:

a = 8 and d = 3

Thus, nth term $\mathrm{= a + (n-1) \times d = 8 + (n-1) \times 3 = 8 + 3n - 3 = 3n + 5}$

Question 2: The sum of the first three terms of an AP is 12 and their product is 60. Find the AP.

Solution:

Using the concept of an AP, let's assume:

The three terms are: $\mathrm{a-d, a, a+d}$

Their sum $\mathrm{= 3a = 12 \Rightarrow a = 4}$

Their product $\mathrm{= (a-d) \times a \times (a+d) = 60}$

From the above, we get a = 4 and d = 2.

Thus, AP is 2, 4, 6,...

Application of Concept 1:

From our previous concept, we learned about APs. We can utilise our understanding of the general form of an AP to find the nth term.

For example, if we recognize a sequence as AP (because of a constant difference), the nth term formula can be directly applied.

Tips and Tricks:

1. Pattern Recognition: If you recognize a sequence of numbers is an AP, then it becomes easier to anticipate the next numbers in the sequence.

2. Shortcut for Common Differences: For quick recognition, subtract consecutive terms. If you obtain the same value consistently, then it’s an AP.

3. Utilise Previous Concepts: As seen in Question 2, sometimes the nth term problem can be disguised in the form of other types of problems. Recognizing the underlying AP helps in quick resolution.

4. Word Problems: In many management entrance tests, AP concepts might be wrapped inside word problems. The key is to break down the problem, identify if the sequence could be AP, and apply the formula.

5. Combining Concepts: In some challenging problems, the concept of AP might be combined with other mathematical concepts like set theory, percentages, or even geometry. Ensure you're comfortable integrating your knowledge.

6. Practice: As is true for most quantitative concepts, practising a wide variety of problems is crucial. With practice, recognizing and solving nth term problems will become second nature.

Remember, every time you encounter an AP problem, think of the basic structure and nature of the progression. This will assist you in tackling even the most challenging problems with ease.