Answer :

Formula Used.


an = a + (n–1)d


a7 = a + (7–1)d


a7 = a + 6d


If 7th term of A.P is given as 18


Then,


a + 6d = 18


we get a = 18–6d ......eq 1


a18 = a + (18–1)d


a18 = a + 17d


If 18th term of A.P is given as 7


Then,


a + 17d = 7


we get a = 7–17d ......eq 2


Equating both eq 1 and eq 2


We get ;


18–6d = 7–17d


17d–6d = 7–18


11d = –11


d = = –1


Putting d in eq 1 we get ;


a = 18–6×(–1)


= 18 + 6 = 24


For 101st term


an = a + (n–1)d


a101 = 24 + (101–1)(–1)


= 24–100


= –76


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