algebra-3

AIEEE 2015 Coaching › Algebra questions › algebra-3

if a₁,a₂....a_2n form a decreasing A.P then

a₁²-a₂²+a₃²-a₄²...............-a_2n²=

a)n(a₁²-a_2n²)/2n-1

b)2n(a₁²-a_2n²)/2n-1

c)2n(a₁²-a_n²)/n-1

d)n(a₁²-a_2n²)/n+1

#Mathematics #Algebra

UP 0 DOWN 0 0 3
Post on FacebookPost anonymously?

3 Answers

1

Ragadeepika ·2009-03-20 22:38:11

a₁,a₂,...a_n are in decreasing AP. It means the common difference is -ve.

Let the common difference be -d.

a₁ - a₂ = a₃-a₄ = ... = d

a₁²-a₂² + a₃² - a₄² + ... -a_2n²

= (a₁ - a₂)(a₁+a₂) + ... + (a_2n-1-a_2n)(a_2n-1+a_2n)

= d(a₁+a₂+...a_2n)

We know that sum of equidistant terms from both ends of an AP is same.

a₁+a_2n

= a₂+a_2n-1=...so on

d(a₁+a₂+...a_2n) = nd(a₁+a_2n) ---1.

a_2n = a₁ + (2n-1)(-d) d = (a₁-a_2n)/2n-1

Putting this in 1, we get the required answer, which is A.
Hope this helps
ALL THE BEST

UP 0 DOWN 0
Post on FacebookPost anonymously?

1

Optimus Prime ·2009-03-20 22:41:03

ya u r rite

UP 0 DOWN 0
Post on FacebookPost anonymously?

11

rkrish ·2009-03-21 00:53:32

SHORTCUT : (to save time)

Let a₁,a₂,...,a_n â‰¡ 3,2,1,0,-1,-2

2n=6 \Rightarrow n=3

Exp = 9 - 4 + 1 - 0 + 1 - 4 = 3 \leftarrow

a) 3(9-4)/6-1 = 15/5 = 3 \leftarrow

b) 6(9-4)/6-1 = 30/5 = 6

c) 6(9-4)/3-1 = 30/2 = 15

d) 3(9-4)/3+1 = 15/4 = 15/4

Hence a is correct

UP 0 DOWN 0
Post on FacebookPost anonymously?

Your Answer

Basic Integral Calculus Operators Symbols Matrix Cases

√ √ || {} [] () → ~ ^ x x x → → ln log lg lim lim cos sin tan cot arcsin arccos arctan

∫ ∫ ∫ ∫ ∫ ∬ ∬ ∬ ∬ ∬ ∭ ∭ ∭ ∭ ∭ ⨌ ⨌ ⨌ ⨌ ⨌

∑ ∑ ∑ ∑ ∑ ∮ ∮ ∮ ∮ ∮ ∏ ∏ ∏ ∏ ∏ ∐ ∐ ∐ ∐ ∐

+ - × ÷ ± ∓ = ∪ ∩ ≠ ∼ ≈ ∅ ∀ ∃ ∈ ∋ ∝ ≤ ≥ ≃ ≅ ≡ < > ≪ ≫ ⊂ ∉ ⊃ ⊆ ⊇ ⇒ ⇐ ⇔ ⇒ ⇐ ⇔ ⇑ ⇓ ⇕ → ← ↔ → ← ↔ ↑ ↓ ↕ ↖ ↗ ↘ ↙ ↪ ↩ ⇀ ↼ ⇁ ↽

° ∂ ∞ α β γ δ θ λ μ ν ξ π ρ σ φ ω ε ƒ κ τ υ Γ Δ Λ Σ Π Ω