# Lesson: Introduction to Sequences

## Comment on Introduction to Sequences

### We need to recognize the

We need to recognize the pattern.
Term 1 has zero 7's in its sum.
Term 2 has one 7 in its sum.
Term 3 has two 7's in its sum.
Term 4 has three 7's in its sum.
Term 5 has four 7's in its sum.
Term 6 has five 7's in its sum.
As we can see, the number of 7's in the sum is 1 less than the term number.
So, for example, term 20 will have nineteen 7's in its sum.
Likewise, term 41 will have forty 7's in its sum.﻿

### https://greprepclub.com/forum

https://greprepclub.com/forum/term-after-the-first-term-is-equal-to-the-preceding-term-1828.html

For the above question in the explanations underneath I am not understanding where the "c" came from.

The question tells us that "In the sequence above, each term after the first term is equal to the preceding term PLUS the constant c."

If a1 is the first term, then:
a2 = a1 + c [add c to the first term]
a3 = (a1 + c) + c [add c to the second term]
.
.
.
etc.

Does that help?

Cheers,
Brent

### Then after getting all the

Then after getting all the way to a5 (which is "a+4c" - is that correct?), when trying to figure out "a1+a3+a5" - why is it that it is "a is MINUS 2c..+2c"

Same with "a2+a4" = "a MINUS c" then everything else is addition...why are we subtracting?

Does that make sense?

### I'm not crazy about that

I'm not crazy about that solution.

Here's my full solution: https://greprepclub.com/forum/term-after-the-first-term-is-equal-to-the-...

Cheers,
Brent

### https://greprepclub.com/forum

https://greprepclub.com/forum/sequence-of-numbers-a1-a2-a3-an-1756.html
How do they cancel out? I don't understand the solution

### I just posted a solution wit

I just posted a solution wit colored fractions to help you see how most of the fractions cancel out: https://greprepclub.com/forum/sequence-of-numbers-a1-a2-a3-an-1756.html#...

Cheers,
Brent

### As mentioned at the video tn=

As mentioned at the video tn= 3n+2 but at the summary of the lesson mentioned in certain sequences some terms are greater than, like example (minute 4:22). So, based on the given data part of the formula (tn= 3n+2 ) works. But, At this example tn= 3 + (40*7 ) the " 3 " is the same as the original formula but why should be added to (40 * 7)? because the term was t41?

Thanks

### Good question.

Good question.
In the first example (at 1:00 of the above video), the first term is denoted as term_0 (aka x_0)

In the second example (at 2:15 of the above video), the first term is denoted as term_1 (aka t_1)

In most cases on the GRE, the first terms of a sequence will be called term_1, but there are times when the first terms is called term_0

Does that help?

Cheers,
Brent