The 20th term of an arithmetic sequence is 101, and the common difference is 3. Find a formula for the nth term.

Question

babynini · Answer

@ganeshie8 are you free? :)

babynini · Answer

hrm, from the info given I have
a_20=a+(20-1)d
a_20=a+(19)*3
a_20=a+57
yeah?

babynini · Answer

@jim_thompson5910 :)

babynini · Answer

we know a_20
so it comes to
101=a+19(3)
a=44

so the formula for the nth term will be
a_n=44+(n-1)(3)
?

jtvatsim · Answer

You've put a lot of work into this already, so let's test your equation to verify it.

jtvatsim · Answer

Testing a_20 seems like a good idea. Do we get the right answer?

jtvatsim · Answer

And.... we do!

jtvatsim · Answer

Looks like you've got it. Congrats!

babynini · Answer

yay! :)

babynini · Answer

thanks for checking ^-^
(how did you test a_20?)

jtvatsim · Answer

Just plugged in n = 20.

jtvatsim · Answer

I hoped it would be 101 as the answer, and it was.

babynini · Answer

oh haha I see. Fabulous.

jtvatsim · Answer

Of course, I needed to see that n = 1 gave me 44 as claimed, but that was kind of obvious since that's what you built the formula to do. :)

babynini · Answer

Indeed :P