Larry claims that 14+12×8+12 and14×12+8×12 are equivalent because they have the same digits and the same operations

They are not the same because one they dont get the same answer and one of the signs are different so it has changed the answer

They are not the same because 14+12=26+8=34×12=168+340=408 and the other one is 14×12=28+140=768 and clearly they are not the same because 768 > 408

2/1 or just 2. sorry if i get this wrong

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

1 the 1st term, 3 the 2nd term, 6 the 3rd term,etc.

note the following:

from the 1st term (1) to the 2nd term (3), we go up by 2,from the 2nd term (3) to the 3rd term (6), we go up by 3from the 3rd term (6) to the 4th term (10), we go up by 4, andfrom the 4th term (10) to the 5th term (15), we go up by 5.

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for