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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