Let Sn represent thestatement, 28+56+112++142n=142n+12, and use mathematical induction to prove that Sn is true for every positive integer n. Follow these steps.

(a) Verify S1.

(b) Write Sk.

(c) Write Sk+1.

(d) Assume that Sk is true and use algebra to change Sk to Sk+1.

(e) Write a conclusion based on Steps(a) to(d).

(a) Verify S1. Write the statement for S1.

S1: 28=

(Do notsimplify.)

Evaluate the right side of S1.

S1: 28=

Is S1 a truestatement?

(b) Write Sk. Write the statement for Sk.

Sk: 28+56+112++142k=

(Do notsimplify.)

(c) Write Sk+1. Write the statement for Sk+1.

Sk+1: 28+56+112++142k+142k+1=

(Do notsimplify.)

(d) Assume that Sk is true and use algebra to change Sk to Sk+1. What should be done to change Sk to Sk+1? Choose the correct answer below.

A.

Add 142k+1 to both sides of Sk.

B.

Add 142n to both sides of Sk.

C.

Subtract 142n from both sides of Sk.

D.

Subtract 142k+1 from both sides of Sk.

Write the expression to change Sk to Sk+1.

28+56+112++142k+142k+1=

14(___2^k+12)

(Simplify youranswer.)

14(2^---- minus 2)

(Simplify youranswer.)

Does the truth of Sk imply the truth of Sk+1? Choose the correct answer below.