Question

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Answer 1

Explanation :

(1) Answer =>

Formula of nth term of GP is given as ;

=> aₙ = arⁿ⁻¹

Here,

• a = 5/2
• r = 1/2

=> a₂₀ = 5/2 × 1/2²⁰⁻¹

=> a₂₀ = 5/2 × (1/2)¹⁹

=> a₂₀ = 5/2²⁰ (Option. 2)

(2) Answer =>

Given that,

• a₈ = 192
• r = 2

• a₈ = 192

=> ar⁸⁻¹ = 192

=> a × 2⁷ = 192

=> a × 128 = 192

=> a = 192/128

=> a = 3/2

Now, we need to find 12th term of GP,

=> a₁₂ = 3/2 × 2¹²⁻¹

=> a₁₂ = 3/2 × 2¹¹

=> a₁₂ = 3/2 × 2048

=> a₁₂ = 3 × 1024

=> a₁₂ = 3072 (Option. 3)

(3) Answer =>

Given,

• a₄ = (a₂)²
• a = -3

• a₄ = (a₂)²

=> ar⁴⁻¹ = (ar²⁻¹)²

=> ar³ = (ar¹)²

=> ar³ = a²r²

=> a = r

Now, we need to find 7th term of GP,

=> t₇ = ar⁷⁻¹

=> t₇ = ar⁶

=> t₇ = -3 × -3⁶

=> t₇ = -3⁷

=> t₇ = -2187 (Option. 1)

Answer 2

Answer:

Explanation :

(1) Answer =>

Formula of nth term of GP is given as ;

=> aₙ = arⁿ⁻¹

Here,

a = 5/2

r = 1/2

=> a₂₀ = 5/2 × 1/2²⁰⁻¹

=> a₂₀ = 5/2 × (1/2)¹⁹

=> a₂₀ = 5/2²⁰ (Option. 2)

(2) Answer =>

Given that,

a₈ = 192

r = 2

• a₈ = 192

=> ar⁸⁻¹ = 192

=> a × 2⁷ = 192

=> a × 128 = 192

=> a = 192/128

=> a = 3/2

Now, we need to find 12th term of GP,

=> a₁₂ = 3/2 × 2¹²⁻¹

=> a₁₂ = 3/2 × 2¹¹

=> a₁₂ = 3/2 × 2048

=> a₁₂ = 3 × 1024

=> a₁₂ = 3072 (Option. 3)

(3) Answer =>

Given,

a₄ = (a₂)²

a = -3

• a₄ = (a₂)²

=> ar⁴⁻¹ = (ar²⁻¹)²

=> ar³ = (ar¹)²

=> ar³ = a²r²

=> a = r

Now, we need to find 7th term of GP,

=> t₇ = ar⁷⁻¹

=> t₇ = ar⁶

=> t₇ = -3 × -3⁶

=> t₇ = -3⁷

=> t₇ = -2187 (Option. 1)

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