Use inductive reasoning to predict the next term in the sequence. -2/3 1/3. -1/6 1/ a -1/2 b -1/12 c -1/18 d -1/24

Question says to use inductive reasoning to predict the next term in the given sequence. -2/3, 1/3, -1/6, 1/12.....

Given sequence can be in AP or GP or any other sequece.

Let's test for GP (Geometric progression)

divide 2nd term by first

similarly divide consecutive terms

all the time we are getting same common ratio -1/2 so that means given sequence is in GP.

Hence we just need to multiply last term by -1/2 to get the

Hence final answer is -1/24.

let x be the money she spent so that she can earn the free t-shirt.

since, she already spent $112.49

⇒

also, as per the statement: jennifer must spend $250 or more in order to qualify for a free t-shirt at the store.

then,

we have an inequality i.,e

subtract 112.49 from both sides we get;

therefore, $137. 51 more money does jennifer need to spend so that she can earn the free t-shirt