Use the Principle of Mathematical Induction to show that the statement is true for all natural numbers n.Use the Principle of Mathematical Induction to show that the statement "5 is a factor of 7n - 2n" is true for all natural numbers. (Hint: 

What will be an ideal response?


When , so the statement is true when . Assume the statement is true for some natural number k. That is,  for some integer m. Then,
 .
So the statement is true for . Conditions I and II are satisfied; by the Principle of Mathematical Induction, the statement is true for all natural numbers.

Mathematics

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Find the first term and the common ratio of the geometric sequence.an = -(1.06)n-1

A. a1 = 1.06, r = 0.06 B. a1 = -1, r = 1.06 C. a1 = -1, r = -1.06 D. a1 = 0, r = (1.06)n-1

Mathematics

Convert the units.417 mL =  L

A. 417,000 L B. 0.417 L C. 4.17 L D. 41,700 L

Mathematics

Write fraction as decimal number. Use bar notation for repeating decimals.

A. 0.9
B. 0.93
C. 0.9375
D. 0.937

Mathematics

Solve the problem.The logistic growth function f(t) =  describes the population of a species of butterflies  after they are introduced to a non-threatening habitat. How many butterflies are expected in the habitat after 16 months?

A. 320 butterflies B. 5120 butterflies C. 480 butterflies D. 278 butterflies

Mathematics