Question

If (5^(k-1))+(5^(k+1)) = m, what is 2*5^k in terms of m?

If
`5^k^-^1+5^k^-^1=m`, what is
`2*5^k` in terms of m?

A) 5m

B) 5m÷2

C) 5m÷13

D) 5m÷26

Answer 1

5m

Explanation:

5^(k-1)+5^(k-1)=m

Going to combine like terms on left:

2×5^(k-1)=m

Law of exponents applied:

2×5^k×5^(-1)=m

Reciprocal:

2×5^k×1/5=m

Multiply 5 on both sides to obtain the requested:

2×5^k=5m