Question

Which of the following shows the correct first step to prove the following by mathematical induction?

3 + 11 + 19 + 27 + … + (8n - 5) = n(4n - 1)

A) 3 + 11 + 19 + 27 + … + (8 • 1 - 5) = 1(4 • 1 - 1)
B) 8 • 1 - 5 = 1(4 • 1 - 1)
C) 3 + 11 + 19 + 27 + … + (8k - 5) = k(4k - 1)
D) 3 + 11 + 19 + 27 + … + (8k - 5) + [8(k + 1) - 5] = (k + 1)[4(k + 1) - 1]

Answer 1

First Step:

Letter Choice (A), 3 + 11 + 19 + 27 + ---- + (8 * 1 - 5) = 1(4 * 1 - 1)


Second Step:

Letter Choice (C), 3 + 11 + 19 + 27 + ---- + (8k - 5) = k(4k - 1)


Third Step:

Letter Choice (D), 3 + 11 + 19 + 27 + ---- + (8k - 5) + [8(k + 1) - 5] = (k +1)[4(k + 1) - 1]



Hope that helps!!!!