If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

### Course: Class 10 (Old)>Unit 5

Lesson 3: nth term of an AP

# Nth term of an arithmetic progression

Let's look at an example problem to learn how to find the nth term of an arithmetic progression. Let's also derive the general expression for the nth term. Created by Aanand Srinivas.

## Want to join the conversation?

• and I dont understand how he says he needs 18 jumps for the 19th term
(1 vote)
• This happens because for the first term (4) you don't need a jump. But from the second term onwards you take one more jump each time. So by the time you reach the 19th term, you would only need 18 jumps because you start jumping at the 2nd term.
• Why is it (n-1)d and not b or c?
• The "d" is supposed to represent the "difference" between each term of the arithmetic sequence. Thus it is denoted by a "d" since the word difference starts with a "d" not a b or c.
• how did he get to the 19th term I dont understand how he got 58 because he did not multiply and he didn't really explain it
(1 vote)
• Well, 18*3 would be 54, and 54+4 would be 58. Same thing with the 23rd term, 22*3 is 66, and 66+4 is 70.

Hope this helps :)
(1 vote)
• If we divide sum of any two term of ap then why we got exactly middle term of this two term?
(1 vote)
• Its bcoz, (Ref=n/2) the sum of any 2 terms of an AP is divided by 2 gets it middle number. example, 3+6/2 is 4.5 which is the middle of these terms and if you multiply 4.5x2 then u will get 9!
(1 vote)
• what would be nth term formula for 4, -9, 16, -25?
(1 vote)
• what if the sequence isnt the same through out ?
(1 vote)
• Then it won't be an arithmetic progression sequence! Simple
(1 vote)
• What is the nth term of the following sequence……… 8, 3, -2, -7………..