The first term of a G. P are as follows: m, m2 +4, 16m. Find the 5th term.

512

Step-by-step explanation:

To effectively answer the question, let us calculate the value of m. This can be obtained as follow:

m, (m² + 4), 16m

1st term (T₁) = m

2nd term (T₂) = m² + 4

3rd term (T₃) = 16m

Common ratio = T₂/T₁ = T₃/T₂

(m² + 4) / m = 16m / (m² + 4)

Cross multiply

(m² + 4)(m² + 4) = m × 16m

(m² + 4)² = 16m²

Take the square root of both side

√[(m² + 4)²] = √(16m²)

m² + 4 = 4m

Rearrange

m² – 4m + 4 = 0

Solving by Factorisation

m² – 2m – 2m + 4 = 0

m(m – 2) – 2(m – 2) = 0

(m – 2)(m – 2) = 0

(m – 2)² = 0

Take the square root of both side

m – 2 = 0

m = 2

Thus,

1st term (T₁) = m = 2

2nd term (T₂) = m² + 4 = 2² + 4 = 8

3rd term (T₃) = 16m = 16 × 2 = 32

The sequence => m, (m² + 4), 16m

Becomes

2, 8, 32

Finally, we shall determine the 5th term. This can be obtained as follow:

1st term (a) = 2

Common ratio (r) = 2nd / 1st = 8/2 = 4

5th term (T₅) =?

T₅ = ar⁴

T₅ = 2 × (4)⁴

T₅ = 2 × 256

T₅ = 512

Therefore, the 5th term is 512

step-by-step explanation:

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