Question

Find t20 for the arithmetic sequence in which t1 = 36 and t3 = 28,

Answer 1

Hey there! I’m happy to help!

We want to look for the twentieth term in this sequence. Because it is arithmetic, this means that the same term will always be added or subtracted.

As we can see, our first term is 36 and then the third is twenty eight. This is a difference of eight, and since our subtracted term will always be the same, we will take this eight and divide it by two, so we can now see that we are subtracting four for each term.

To find the twentieth term, you could count, but that would be a hassle. You can also use the arithmetic sequence formula, which I will show below.

You take the desired term (20)

Subtract 1 (19)

Multiply it by the common term/difference (19*-4=-76)

And then add the first number of the sequence (-76+36= -40)

You can now do those exact same steps for any arithmetic sequence you are dealing with!

So, your twentieth term is -40!

I hope that this helps!