12,20,28,...
Find the 35th term.

284

Step-by-step explanation:

This is an arithmetic sequence because these terms, when subtracted the next term with previous term, we get the same difference.

20-12 = 8

28-20 = 8

Because all terms’ difference are same, we call it common difference.

A common difference is shortly given as ‘d’ and from the sequence, our common difference is 8.

Do you know? If a sequence has common difference, it is an arithmetic sequence.

Next, we want to find the 35th term. That’s too far and no one is going to add the term up with the common difference since that takes too much time, which is why a formula makes it easier to calculate.

Arithmetic General Term

where a_n is nth term, a1 is first term and d is common difference.

We know a1 is 12 and d is 8, substitute them in.

Since we want to find 35th term, substitute n = 35.

Therefore, the 35th term of this sequence is 284.

n=9

step-by-step explanation:

7 times a number = 7n

decreased by 13 = 7n-13

same as is =

5 times the number = 5n

increased by 5 = 5n+5

7n-13 = 5n+5

2n=18

n=9