QUESTION 12Solve the problem.Suppose you wish to prove the statement that follows using mathematical induction.5 + 8 + 11 ++ (3n+ 2)(3n+ 7), for all positive integers n.Let S, be the statement 5+ 8+ 11 + ... + (3n+ 2):(3n+7). Show that S, is true.=Since (3(1) + 2) = 5, S, is true.Since (3(1) + 7) =(10) = 5, S, is true.2Since 5 + 8 = 13 ==(3(2)+ 7), S, is true.Since 5 +(3(1) + 2) =5(5 + 3(1) + 2), S, is true. QUESTION 11Find the indicated term of the binomial expansion.(x - y)16; seventh termO -8008x10y6O 11,440xºy7O 8008x10y6O-11,440x°y7

Since you have asked multiple question, we will solve the first question for you as per our guide…

QUESTION 12 Solve the problem. Suppose you wish to prove the statement that follows using mathematical induction. 5+ 8 + 11 + ... + (3n+ 2) (3n+ 7), for all positive integers n. 2 Let S, be the statement 5 + 8+ 11 + ... + (3n+ 2) =(3n+ 7). Show that S, is true. Since (3(1) + 2) = 5, S1 is true. Since (3(1) 3(1) + 7)=(10) = 5, Sq is true. Since 5 + 8 = 13 =;(3(2)+7), S, is true. Since 5 +(3(1) + 2) : (5 + 3(1)+ 2), S, is true.