Sequence and Series

General Instructions for Candidates

• Do not open booklet until instructed.
• Test duration: 1 hour.
• Fill in necessary information on the provided space and answer sheet before exam commencement.
• Use only an HB pencil to darken the answer circles.
• One mark is awarded for each correct answer.
• 1/4 mark will be deducted for each incorrect answer.
• Multiple darkened circles for one question will be marked wrong.
• Questions left unanswered i.e. blanks, will be given a zero.
• Rough work must only be done on pages specified as "SPACE FOR ROUGH WORK."
• Correct marking method: Darken the circle corresponding to the correct answer.

Paper-2 Topics

• Sequence & Series
• Indices
• Equations
• Maximum Marks: 50

Key Concepts

Question 1

• Find two numbers where Geometric Mean = 5 and Arithmetic Mean=7.5

Question 2

• Calculating Zero Sum: You sum the series 50 + 45 + 40 + 35 + ... to zero, find number of terms.

Question 3

• Installment Payments: A person pays Rs. 975 in monthly installments decreasing by Rs. 5 each month, from an initial installment of Rs. 100; the task is to determine the payment duration.

Question 4

• Ratio of Sums: Determine the ratio between the sum of the first 'n' natural numbers and the sum of cubes of the first 'n' natural numbers.

Question 5

• Arithmetic Progression (AP): If the 𝑝th term of an AP is 'q' and the 𝑞th term is 'p', find its 𝑟th term.

Question 6

• Summing a Series: Find the value of 'x' if 2 + 6 + 10 + 14 + 18 + ... + x = 882, where the series is arithmetic.

Question 7

• 1 1 1
• Series Summation: Sum the series 5 , 52 , 53 ⋯ ⋯ ⋯ 5n

Question 8

• Ratio of Sums of APs: If the ratio of the sum of n terms of two APs is (n+1):(n-1), find the ratio of their mth terms.

Question 9

• Geometric Progression: Given that the 5th term of a GP is 27 and the 8th term is 729, compute the 11th term.

Question 10

• Sum of AP Terms: The sum of n terms of an AP is 3𝑛² + 𝑛; determine the 𝑝thterm.

Question 11

• 1 1 1
• Sum of Fractions: Find the largest value of n for which 2 + 22 +…. 2n < 0.998.

Question 12

• Ratio of Arithmetic Series Sums: You have the equation (1+3+5+...+𝑛 terms)/(2+4+6+...+ 50 terms)=2/51; your job is to find 'n'.

Question 13

• Geometric Progression (GP) Sum: The sum of the first 8 terms of a GP is five times the sum of the first 4 terms; determine the common ratio.

Question 14

• Nth Term: If the 𝑛th term of an AP series is 7n – 2, find the sum of 'n' terms.

Question 15

• Infinite Geometric Series: Given an infinite geometric series with the first term 'a', common ratio 'r', a sum of 4, and a second term of 3/4, determine the correct combination of 'a' and 'r'.

Question 16

• Finding a Term in Arithmetic Progression: Determine the 20th term of an arithmetic progression given that the 6th term is 38 and the 10th term is 66.

Question 17

• 1
• Identify Terms: If series is 25, 5, 1 find number of terms in series if final term is 3125

Question 18

• Geometric Progression (GP): Given that the sum of first 20 terms of a GP is 1025 times the sum of its first 10 terms, find the common ratio.

Question 19

• Exponential Equation Relationships: If 2𝑎 = 3𝑏 = 12𝑐, calculate 1/𝑎 + 1/𝑏 value

Question 20

• Exponential Expressions: If px = q, qy = r, and rZ = p6, determine the value of xyz.

Question 21

• Equation Evaluation: Given a=(√5+√3)/(√5−√3)) and b=(√5−√3)/(√5+(√3)), find the value of a²+b².

Question 22

• Radical Simplify: Determine the value of (1 − √0.027(5/6)(2/3))

Question 23

• Solving for x in Equations: If (3a/2b)^(2x-4)= (2b/3a)^(3a) for some a, b, you must find the value of 'x'.

Question 24

• Exponential Variable Relationships: If 2𝑥 = 3𝑦 = 6 𝑧, what does 1/x + 1/y equal?

Question 25

• 2𝑛+2𝑛−1
• Exponential Simplification: Simplify 2𝑛+1 +2𝑛

Question 26

• Algebraic Equations: If 𝑥 = 51/3 + 5−1/3, find the value of 5𝑥³ − 15𝑥.

Question 27

• Variable Relationship: If P = x1/3 + x −1/3, then calculate what P³ = 3P equals.

Question 28

• 𝑥 = √√6 + 6 + (√7 + 2√6) − √6: Find the value
• Find the value of 'x'. If x = √√6 + 6 + (√7 + 2√6) − √6

Question 29

• Variable: Finding Value: If 𝑝𝑞𝑟 = 𝑎 𝑥 , 𝑞𝑟𝑠 = 𝑎 𝑦 , and 𝑟𝑠𝑝 = 𝑎 𝑧, what's the value of (𝑝𝑞𝑟𝑠)1/2?

Question 30

• Age Calculation: The present age of a man exceeds thrice the sum of the ages of his twin grandsons by 8 years. After 8 years, his age will exceed twice the sum of the grandsons' ages by 10 years.

Question 31

• Quadratic Equation Roots: If α + β = -2 and αβ = -3, find the quadratic equation with roots α and β.

Question 32

• Roots of Quadratic: If the roots of 4𝑥² − 12𝑥 + 𝑘 = 0 are equal, calculate value of 'k''.

Question 33

• Cubic Equation Roots: Find the roots of the cubic equation 𝑥³ − 7𝑥 + 6 = 0.

Question 34

• Find x² − 10𝑥 + 1: Determine given x = 5−2√6

Question 35

• Quadratic Equation: Identify equation if two roots are, α, 1/α respectively

Question 36

• Root Evaluation: If roots of the equation 𝑥² + 7𝑥 + 12 = 0 is α and β, Calculate α²/β +β²/α.

Question 37

• Exponential Values: Solve for X and Y if 2𝑥+𝑦 = 22𝑥−𝑦 = √8.

Question 38

• Equilateral Triangle Side Length: The sides of an equilateral triangle are shortened by 3, 4, and 5 units, forming a right triangle; what was the original side length of the equilateral triangle?

Question 39

• Quadratic Equation: Find the value of P, difference = 2, roots of equation 𝑥² + 𝑝𝑥 + 8 = 0.

Question 40

• Identify Harmonic Mean: Harmonic mean for equation (5 + √2)𝑥² − (4 + √5)𝑥 + 8 + 2√5 = 0

Question 41

• Algebra: 2 oranges and 3 apples costs Rs. 28. 3 oranges and 5 apples costs Rs. 75. The value of 7 oranges and 4 apples.

Question 42

• If roots of x² - px + q = 0 are in the ratio 2:3

Question 43

• The longest side of a triangle is 3 x the shortest side, with the third side 4 cm less than the longest. If the perimeter is over 59 cm, find the shortest side.

Question 44

• Multiple Choice: Find the difference between right and wrong answers. 100 questions, 1 mark each, 60% marks, penalty = 0.25.

Question 45

• Duration of tour: A traveler with Rs. 9,600 shortens his tour by reducing Rs. 20 in daily expenses by after extending 16 days. Find original duration.

Question 46

• If roots of 𝑥² − 𝑘𝑥 + 8 = 0 differ by 4, identify the possible value of K

Question 47

• Determine Quadratic Equation

Question 48

• Real Root If: Real root conditions of 𝑥² + (2𝑝 − 1)𝑥 + 𝑝 = 0 equation.

Question 49

• Point Lie: Determine which quadrant the intersection point of 3𝑥 + 4𝑦 = 7 and 4𝑥 – 𝑦 = 3 lies

Question 50

• Root of equation equation 𝑥² − 𝑥 + 1 = 0
• Are the roots of the equation Real or Imaginary? Unequal or Equal?