CAT To find the sum of n terms of an AP MCQ - Practice Questions & Answers

Quick Facts

3 Questions around this concept.

Solve by difficulty

EASY

Find 6 + 9 + 12 + . . . + 30.

160

165

162

125

View Solution

Concepts Covered - 1

To find the sum of n terms of an AP

Formula to find the sum of the first n terms of an AP:

$\mathrm{S_n=\frac{n}{2}[2 a+(n-1) \times d]}$

Where:

- $\mathrm{S_n}$ is the sum of the first n terms

- a is the first term

- d is the common difference

- n is the number of terms

Another formula, especially useful when the first and the last term are known:

$\mathrm{S_n=\frac{n}{2}\left(a_1+a_n\right)}$

Where $\mathrm{a_1}$ and $\mathrm{a_n}$ are the first and nth terms respectively.

Foundation Building Questions:

Question 1: The first term of an AP is 3, and the common difference is 2. Find the sum of the first 20 terms.

Solution:

Using the formula:

$\mathrm{S_n=\frac{n}{2}[2 a+(n-1) \times d]}$

For n=20, a=3, and d=2:

$\mathrm{S_{20}=\frac{20}{2}[2(3)+(20-1) \times 2] }$

$\mathrm{S_{20}=10 \times[6+38]=10 \times 44=440 }$

Question 2: If the sum of the first 10 terms of an AP is 65 and the sum of the next 10 terms is 165, find the AP.

Solution:

Let's assume the first term is a and the common difference is d.

For first 10 terms:

$\mathrm{S_{10}=\frac{10}{2}[2 a+(10-1) \times d]=65 }$

For next 10 terms (from 11th to 20th term):

$\mathrm{S_{10}=\frac{10}{2}[2(a+10 d)+(10-1) \times d]=165}$

From these equations, we can derive the values of a and d and thus, find the AP.

Application of Previous Concepts:

The application of the sum formula can be combined with the formula to find the nth term of the AP. For instance, to determine the nth term, we can subtract the sum of the first (n-1) terms from the sum of the first n terms.

Tips and Tricks:

1. Break down series: Sometimes, the sum of the entire series might not be directly asked. Instead, it might be broken down into parts (e.g., sum of first 10 terms, next 10 terms). Recognize these patterns and tackle each section of the series separately.

2. Mix of Formulas: The formula for sum using the first and nth terms can be especially useful in scenarios where the last term is given or can be easily found.

3. Visual Representation: Draw a quick number line or series to visualise the problem better. Sometimes seeing the series visually can help spot patterns or shortcuts.

4. Application in Real Life Scenarios: Management exams often use real-life scenarios for questions. Think of AP applications in real-world situations like savings, recurring deposits, investments, etc.

5. Integration with Other Concepts: Remember, the problem might not just be about AP. It could be a combination of various concepts like algebraic equations, percentages, or even geometry. Familiarise yourself with such combined problems.

6. Double-check calculations: With sum problems, there's a lot of arithmetic involved. A small mistake can lead to incorrect answers, especially in multiple-choice questions where incorrect options are designed based on common errors.

Remember to always approach AP sum problems methodically, understanding the problem's requirements first, and then applying the appropriate formula or strategy. As with other topics, consistent practice will enhance speed and accuracy.