Answer :

The two-digit numbers that are divisible by 7 are 14, 21,….. ,98


Here, First term = a = 14


Common difference d = 21 – 14 = 7,


Last term = an = 98


Since, nth term is given by:


an = a + (n - 1) d


98 = 14 + (n – 1)7


98 = 14 + 7n – 7


98 = 7 + 7n


91 = 7n


n = 13


There are 13 two-digit numbers divisible by 7.


OR


We know sum of n terms of an AP is:


Sn = n2


For n = 1,


S1 = 12


= 1


For n = 2,


S2 = 22


= 4


For n = 3,


S3 = 32


= 9



Now S1 = a1


a1 = 1


S2 – S1 = a2


4 – 1 = a2


3 = a2


Now, d = a2 – a1
= 3 -1


= 2


We know, an = a + (n – 1)d


For n = 10,


a10 = 1 + (10– 1)2


= 1 + 9(2)


= 1 + 18


= 19


So, 10th term of the AP is 19.


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