Arithmetic Progression: Term & Sum
Arithmetic Progressions · Class X
Choose first term a, common difference d, and term count n; get nth term and total sum.
- n-th term29
- Sum of n terms155
- Average of n terms15.5
- a_n as a function of n
Formulas in this lab
- n-th term
- Sum of n terms
- Average of n terms
Frequently asked questions
▶What is the formula for an AP?
An arithmetic progression has first term $a$ and common difference $d$. The nth term is $a_n = a + (n-1)d$ and the sum of the first n terms is $S_n = \frac{n}{2}[2a + (n-1)d]$. For a = 3, d = 5, the fourth term is 18.
▶How do I use this lab?
Slide a, d and n. The lab displays the nth term and the running sum side by side. Try a = 2, d = 3, n = 10 to see $a_{10} = 29$ and $S_{10} = 155$.
▶Common mistake on this topic
Students write $a_n = a + nd$ instead of $a + (n-1)d$, getting an answer that is one step too far. Also, mixing up $a_n$ (a single term) with $S_n$ (a sum) costs easy marks in board exams.
▶Where do we see APs in real life?
Saving Rs 100 the first month, Rs 150 the next, Rs 200 after, and so on is an AP. Seats in an auditorium row, EMIs that increase by a fixed amount, and theatre rows widening by a constant are all APs.