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Class 9 · Mathematics worksheetExploring some more Progressions (Advanced)
CBSE Mathematics. Optional Advanced level: sum of a GP, infinite GPs, bouncing balls and nested squares, the method of differences for nth terms and sums. Every sheet has 20 questions in three sections and an answer key, and the numbers change every time.
Sample questions
Real questions from this chapter, as the app sets them. Tap Answer to see the answer and working.
Section A · multiple choice
- 1.
The sum of the first 8 terms of 1, 3, 9, … is:
- 6,560
- 6,561
- 9,841
- 3,280
Answer
(d) 3,280
a(rⁿ − 1)/(r − 1) = 1(3⁸ − 1)/2
- 2.
The sum to infinity of the GP 19, −76/5, 304/25, … is:
- 171/5
- 95
- 104/9
- 95/9
Answer
(d) 95/9
a ÷ (1 − r) = 19 ÷ (1 − (−4/5))
- 3.
The sum of the first n terms of a GP with first term a and ratio r ≠ 1 is:
- n(a + arⁿ) ÷ 2
- arⁿ ÷ (1 − r)
- a(1 − r) ÷ (1 − rⁿ)
- a(1 − rⁿ) ÷ (1 − r)
Answer
(d) a(1 − rⁿ) ÷ (1 − r)
subtract rSₙ from Sₙ
Section B · short answer
- 4.
Find the exact sum of the first 8 terms of the GP 24, 12, 6, …
Answer
765/16
a(1 − rⁿ)/(1 − r) = 24(1 − (1/2)⁸) ÷ (1 − (1/2))
- 5.
Use differences to find the nth term of 10, 24, 46, 76, 114, …, and hence its 12th term.
Answer
tₙ = 4n² + 2n + 4; t₁₂ = 604
b = 10, a = 14, d = 8; tₙ = b + a(n − 1) + d(n − 1)(n − 2)/2
Section C · long answer
- 6.
A square of side 24 cm is cut from card. The midpoints of its sides are joined to make a second square, which is cut and pasted on it, and so on. Find (a) the area of the 8th square (b) the total area of card for the first 8 squares (c) the total area if this went on forever.
Answer
(a) 9/2 cm²; (b) 2295/2 cm²; (c) 1,152 cm²
the areas form a GP 576, 288, … with r = 1/2; (b) 576(1 − (1/2)⁸) ÷ (1/2); (c) 576 ÷ (1 − 1/2)
Fresh sheets for your child
In the app, every Exploring some more Progressions (Advanced) sheet is new: the app remembers the questions your child has already had and leaves them out. Print the sheet as a PDF, or use notebook mode and write the answers in a notebook.
Coming soon for Android and iPhone.