Question

Can you check my answer?

Which of the following shows the best next step to prove the following by mathematical induction?

1+4+7+10 + + (3n-2)=n/2(3n-1)

1.When n=1, the formula is valid because
(3*1-2)=1/2(3*1-1)
(3-2)=1/2(3-1)
1=1/2(2)
1=1

A. You must show that 1+4+7+10 + + (3(k+1)-2)=k/2(3(k+1-1)

b.You must show that 1+4+7+10 + + (3k-2)+(3(k+1)-2)=k+1/2 (3(k+1)-1)

c. Assuming that 1+4+7+10 + + (3k-1)=k/2(3k-1)

d. Assuming that 1+4+7+10 + + (3(k+1)-1)=k/2(3k-1)

answer:d

Answer 1

I pick D.

Then you have to add a term to both sides:

1+4+7+10 + + (3k-2)+(3(k+1)-2) = k/2 (3k-1) + (3(k+1)-2)

and then show that

k/2 (3k-1) + (3(k+1)-2) = (k+1)/2 (3(k+1)-1)

watch the parentheses when working online. Things can be misread due to the lack of text formatting.