General term of arithmatic progression

Jun 16, 2020, 16:45 IST

General term of arithmatic progression

Definiton :-This general term is the formula that is used to calculate any number in an arithmetic sequence.
The formula tells us that if we wanted to find a particular number in our sequence, xn, we would take our beginning number, a, and add our common difference, d, times n minus 1, which is the location of our desired number minus 1. If we are looking for the 30th number, our n is 30, so our formula begins with x30, and n - 1 equals 29 (30 - 1).

Formula description :-

Practical appication :-
The general term is the formula that is used to calculate any number in an arithmetic sequence.

Example: A person started his physical workout with just 15 min. Duration and he keeps enhance his duration of 2 min on every next day. If would like to know the duration of his workout on 18th day then it would be

Example 1 :-Which term of the sequence 6, 11, 16, 21, 26, ....... Is 126?

Solution :-
let 126 is the nth term of the given sequence. Then,
Ann = 126
⇒ a + (n - 1)d = 126
⇒ 6 + (n - 1) × 5 = 126
⇒ 6 + 5n - 5 = 126
⇒ 5n + 1 = 126
⇒ 5n = 126 - 1
⇒ 5n = 125
⇒ n = 25
Hence, 25th term of the given sequence is 126.

Example 2 :-

Solution :-
We has am = a + (m – 1) d= n, .….(1)
And …..(2)
Solving (1) and (2), we get
(m – n) d = n – m, or d = – 1, …..(3)
And a = n + m – 1 …..(4)

Therefore = n + m – 1 + (p – 1) (–1) = n + m – p

Hence, the pth term is n + m – p.