# Act.al.4 What is the 50th term

• MHB
• karush
In summary, the 50th term of the given arithmetic sequence is 248. This can be found by using the formula $a_n = a_1 + (n - 1)d$, where $a_1= 3$ and $d= 5$.
karush
Gold Member
MHB
$\tiny{act.al.4}$
The 3rd and 4th terms of an arithmetic sequence are 13 and 18, respectively. What is the 50th term of the sequence?
$a.\ {248}\quad b.\ {250}\quad c.\ {253}\quad d.\ {258}\quad e.\ {263}$

ok according to Sullivan's textbook
$a_1=a\quad a_n=a_{n-1}+d$
so $d=5$ and $a_1=3$
and the nth term is
$a_n = a_1 + (n -1)d$
then
$a_50= 3+ (50 -1)5=$ 248

Last edited:
Yes, since two consecutive terms are 13 and 18, d, the "common difference", is 18- 13= 5. Calling the first term $a_1$, the second difference is $a_2= a_1+ 5$ and the third difference is $a_1+ 10= 13$ so that $a_1= 13- 10= 3$. Well done!

And then the 50th term is the first term, $a_1= 3$, plus d= 5, added 50- 1= 49 times. 49 times 5= 245. The 50th term is 3+ 245= 248, exactly what have! Excellent!

mahalo,

I assume $a_1$ never goes negative

the hard part is trying to remember these formulas

Last edited:
DON'T memorize formulas, memorize definitions! Everything I wrote follows directly from the definition of "arithmetic sequence".

## 1. What is the meaning of "Act.al.4"?

Act.al.4 refers to the fourth term in an arithmetic sequence, where each term is obtained by adding a constant value to the previous term.

## 2. How do you determine the 50th term in an arithmetic sequence?

The 50th term in an arithmetic sequence can be found by using the formula: an = a1 + (n-1)d, where an is the nth term, a1 is the first term, and d is the common difference between terms.

## 3. What is the common difference in an arithmetic sequence?

The common difference in an arithmetic sequence is the constant value that is added to each term to obtain the next term in the sequence.

## 4. How can you identify an arithmetic sequence?

An arithmetic sequence can be identified by looking for a consistent difference between each term in the sequence. Each term will have the same amount added to it to get to the next term.

## 5. Can the 50th term in an arithmetic sequence be negative?

Yes, the 50th term in an arithmetic sequence can be negative if the common difference and first term are both negative, or if the common difference is negative and the first term is positive but has a smaller absolute value than the common difference.

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