Score 90+ in FBISE Class 11 Math Unit 4 – all exercises key answers!
HSA Notes Features
- 100% NBF/FBISE accurate
- Exercises 4.1–4.8 + Review solved
- Short, exam-ready format
- Updated 2025-2026 syllabus
- Arithmetic, geometric, harmonic progressions
- Sigma notation & infinite sums
- Free PDF with diagrams
- Trusted for top marks
Target Audience
FBISE + Punjab boards. Top schools: Beaconhouse, Roots, LGS, City School, Karachi Grammar, Aitchison, Lawrence, ICG, APS, FPS.
Unit 4 Key Solved Highlights
Ex 4.1 (General Term)
Q1(i) 4,7,10,13; a₁₀=31, a₁₅=46
Q1(ii) 2,5,8,11; a₁₀=29, a₁₅=44
Q1(iii) ½,⅔,¾,⅘; a₁₀=10/11, a₁₅=15/16
Q1(iv) 2,5,10,17; a₁₀=101, a₁₅=226
Q1(v) -1,0,3,8; a₁₀=80, a₁₅=195
Q1(vi) 0,3/5,4/5,15/17; a₁₀=99/101, a₁₅=112/113
Q1(vii) 1,-½,¼,-⅛; a₁₀=-1/512, a₁₅=1/16384
Q1(viii) -1,4,-9,16; a₁₀=100, a₁₅=-225
Q1(ix) -4,5,-6,7; a₁₀=13, a₁₅=-18
Ex 4.2 (A.P.)
Q1(i) 4,7,10,13
Q2(i) 17,21,25
Q4 19,16.5,14,11.5
Q5 8,5,2,-1,-4
Q7 n=20
Q10 a₈=240 ft
Q11 S₂₀=400000 Rs
Ex 4.3 (A.P. Sum)
Q1 S₈=116
Q8 S₅₀=2550 (even 2 to 100)
Q9 S₅₀=2500 (odd 1 to 99)
Q17 S₁₆=816
Q23 S₂₅=950 marchers
Ex 4.4 (G.P.)
Q3 r=3/2
Q5 3,-6,12,-24
Q8 10/3, 10/9
Q14 a₃=100
Q20 Means: 6,12,24
Ex 4.5 (G.P. Sum)
Q1 S₁₁=176
Q2 ≈93.75
Q15 Total distance=70 ft
Q16 Max height=800 ft
Ex 4.6 (H.P.)
Q1 7th term=1/27
Q7 14th term=1/43
Q10 H.M.=9.9; A=10, G=3√11, AH=G²
Ex 4.7 (Sigma & Formulas)
Q1 31/32
Q7 43
Q8 10/11
Q13 ∑k³ = [n(n+1)/2]² proved
Ex 4.8 (Applications)
Q1 780 ft
Q2 1065 seats → No
Q3 491700 Rs
Q4 Day 20: 524288 Rs
View PDF for full solutions, diagrams, proofs.
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