General Term of an Arithmetic Progression

Choose the correct alternative answer for the following sub question

If third term and fifth term of an A.P. are 13 and 25 respectively, find its 7^th term

Find t_n if a = 20 आणि d = 3

Find t₅ if a = 3 आणि d = −3

Decide whether the given sequence 24, 17, 10, 3, ...... is an A.P.? If yes find its common term (t_n)

How many two-digit numbers are divisible by 5?

Activity :-  Two-digit numbers divisible by 5 are, 10, 15, 20, ......, 95.

Here, d = 5, therefore this sequence is an A.P.

Here, a = 10, d = 5, t_n = 95, n = ?

t_n = a + (n − 1) `square`

`square` = 10 + (n – 1) × 5

`square` = (n – 1) × 5

`square` = (n – 1)

Therefore n = `square`

There are `square` two-digit numbers divisible by 5

Decide whether 301 is term of given sequence 5, 11, 17, 23, .....

Activity :-  Here, d = `square`, therefore this sequence is an A.P.

a = 5, d = `square`

Let n^th term of this A.P. be 301

t_n = a + (n – 1) `square`

301 = 5 + (n – 1) × `square`

301 = 6n – 1

n = `302/6` = `square`

But n is not positive integer.

Therefore, 301 is `square` the term of sequence 5, 11, 17, 23, ......

12, 16, 20, 24, ...... Find 25^th term of this A.P.

If t_n = 2n – 5 is the nth term of an A.P., then find its first five terms