Q. 14.0( 6 Votes )

# Write the algebraic expression for each of the sequences below:

i) Sequence of odd numbers

ii) Sequence of natural numbers which leave remainder 1 on division by 3.

iii) The sequence of natural numbers ending in 1.

iv) The sequence of natural numbers ending in 1 or 6.

Answer :

i) Sequence of odd numbers-

Odd numbers are those which are not divisible by 2

i.e. 1, 3, 5… and so on

i.e. (2-1),(4-1),(6-1)…and so on

Thus **Sn = 2n-1**, where n = 1, 2, 3… and so on

ii) Sequence of natural numbers which leave remainder 1 on division by 3. -

Dividend = (Divisor × Quotient) + (Remainder)

Here, Divisor = 3

Remainder = 1

For getting the required sequence, putting quotient as 1, 2, 3… and so on

Dividend = 4,7,10…

i.e. **Sn= 3n + 1**

iii) The sequence of natural numbers ending in 1.

Natural numbers ending in 1 are 1, 11, 21… and so on

These can be written as (10-9),(20-9),(30-9),… and so on

Hence, the sequence **Sn = 10n-9** where n = 1, 2, 3… and so on

iv) The sequence of natural numbers ending in 1 or 6.

The natural numbers ending in 1 or 6 are 1, 6, 11, 16, 21…and so on

Observing the pattern, these numbers can be written as (5-4), (10-4), (15-4),…and so on

Hence, the sequence **Sn = 5n-4**, where n = 1, 2, 3… and so on

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