Maths · Algebra · chapter 8 of 14
Class 11 Maths Chapter 8: Sequences and Series case study question with answers
One case-based question of the kind CBSE-pattern school exams ask: a passage, then 3 parts worth 4 marks in all, with the answer and the marking scheme for each. Written from the NCERT chapter.
Case study · 4 marks
In a science club in Kochi, students fold a sheet of paper 0.1 mm thick in half again and again. Each fold doubles the thickness of the folded stack and halves the area of its top face. The sheet starts with a top face of area 600 cm². The students record the thickness after each fold, 0.2 mm, 0.4 mm, 0.8 mm, …, and notice that the thicknesses and the areas each form a geometric progression.
Part 1 · 1 mark
The thickness of the stack after 6 folds is
Show answer
Answer: (c) 6.4 mm
Thickness after n folds = 0.1 × 2n mm, so after 6 folds it is 0.1 × 64 = 6.4 mm.
Part 2 · 1 mark
The least number of folds after which the stack is more than 10 cm thick is
Show answer
Answer: (b) 10
10 cm = 100 mm: 0.1 × 2n > 100 needs 2n > 1000; 29 = 512, 210 = 1024, so n = 10.
Part 3 · 2 marks
Find the area of the top face after 5 folds, and the least number of folds after which it is less than 1 cm².
Answer and marking scheme
Area after n folds = 600 × (1/2)n cm². After 5 folds: 600/32 = 18.75 cm². 600/2n < 1 needs 2n > 600; 29 = 512, 210 = 1024, so after 10 folds.
- area after 5 folds = 18.75 cm² (1)
- 10 folds (1)
Or
A second sheet, 0.2 mm thick, is folded in three each time, so its thickness triples at every fold. After how many folds is it first thicker than the first sheet after 10 folds?
Answer and marking scheme
The first sheet after 10 folds is 0.1 × 210 = 102.4 mm. The second after n folds is 0.2 × 3n mm, and 0.2 × 3n > 102.4 needs 3n > 512. 35 = 243 and 36 = 729, so after 6 folds (145.8 mm).
- 102.4 mm for the first sheet and 0.2 × 3^{n} for the second (1)
- 6 folds (1)