Answer:
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
