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

the answer to the expression is 83

not only in mathematics, scientific proof also are required in the other field of science. also maths proofs are of particular structure, containing steps and logics. so proving is like doing science, it is science. that's why it is important to prove. 

an inaccurate proof leads to errors, or stating results that are not accurate.  which wil mess the probelm up you dont want this