General Term of an Arithmetic Progression

In an A.P. if the sum of third and seventh term is zero. Find its 5^th term.

Find a and b so that the numbers a, 7, b, 23 are in A.P.

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, ......

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 the following sequence is an A.P., if so find the 20^th term of the progression:

–12, –5, 2, 9, 16, 23, 30, ..............

Choose the correct alternative answer for the following sub-question

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

Find the sum of the following arithmetic series:

(-5)+(-8)+(-11)+...+(-230)

Find the sum of  the following arithmetic series:

`7 + 10 1/2 + 14 + ....... + 84`