Sequences, Progressions and Patterns Short Notes for XAT: Concepts, Formulas, Worked Examples & Practice

Sequences, Progressions and Patterns short notes for XAT: 1 study cards covering concepts, formulas, shortcuts and exam traps, plus solved practice questions.

Summary: Quick Formula & Pattern Recall

Quick Recall

A.P. Formulas

$a_{n} = a + (n - 1) d$
$S_{n} = \frac{n}{2} [2 a + (n - 1) d]$

G.P. Formulas

$a_{n} = a \cdot r^{n - 1}$
$S_{\infty} = \frac{a}{1 - r}$ ( $∣ r ∣ < 1$ )

Exam Heuristics

Bouncing Object: Total distance = $H + 2 \times$ (Sum of bounces).
$a_{n + 1} = \frac{1}{1 + a _{n}}$ : Invert to $\frac{1}{a _{n + 1}} = 1 + a_{n}$ .
Nested Functions: Build a table from base case $f (0, y)$ outwards.
Sum except $i$ -th: Replace with $S_{t o t a l} - a_{i}$ .
Interleaved A.P.s: Diff = $\frac{End _{2} - End _{1}}{Gaps}$ .

Sequences, Progressions and Patterns: Solved Questions with Step-by-Step Explanations (2 Problems)

Question 1 · Quantitative Aptitude and Data Interpretation (QA & DI) MCQ

In an arithmetic progression, the first term is 7 and the common difference is 4. What is the value of the 12th term?

A.
51
B.
48
C.
55
D.
44

Correct Answer:

Step-by-Step Solution

Key idea: This is a direct application of the Arithmetic Progression (A.P.) $n$ -th term formula.

Step 1: Identify the given values. The first term $a = 7$ , the common difference $d = 4$ , and the term number $n = 12$ .

Step 2: Recall the formula for the $n$ -th term of an A.P.: $a_{n} = a + (n - 1) d$ .

Step 3: Substitute the values into the formula.

$a_{12} = 7 + (12 - 1) \times 4$

$a_{12} = 7 + 11 \times 4$

$a_{12} = 7 + 44 = 51$ .

Answer: 51

Question 2 · Quantitative Aptitude and Data Interpretation (QA & DI) MCQ

What is the sum of the first 10 terms of an arithmetic progression where the first term is 3 and the common difference is 2?

A.
120
B.
100
C.
130
D.
110

Correct Answer:

Step-by-Step Solution

Key idea: This is a direct recall and application of the Arithmetic Progression (A.P.) sum formula.

Step 1: Identify the given values. The first term $a = 3$ , the common difference $d = 2$ , and the number of terms $n = 10$ .

Step 2: Recall the formula for the sum of the first $n$ terms of an A.P.: $S_{n} = \frac{n}{2} [2 a + (n - 1) d]$ .

Step 3: Substitute the values into the formula.

$S_{10} = \frac{10}{2} [2 (3) + (10 - 1) 2]$

$S_{10} = 5 [6 + 9 (2)]$

$S_{10} = 5 [6 + 18]$

$S_{10} = 5 [24] = 120$ .

Answer: 120

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Sequences, Progressions and Patterns Short Notes for XAT: Concepts, Formulas, Worked Examples & Practice

Sequences, Progressions and Patterns short notes for XAT: 1 study cards covering concepts, formulas, shortcuts and exam traps, plus solved practice questions.

A question from this chapter

Question 1

In an arithmetic progression, the first term is 7 and the common difference is 4. What is the value of the 12th term?

Question 2

What is the sum of the first 10 terms of an arithmetic progression where the first term is 3 and the common difference is 2?

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