Q. 84.5( 2 Votes )

The 10th and 18th terms of an A.P are 41 and 73 respectively. Find the 27th term.

Answer :

Here, t10 = 41 and t18 = 73


We know that nth term of A.P. , tn = a + (n – 1) d.


First, t10 = a + (10 – 1) d = 41


a + 9d = 41 … (1)


Then, t18 = a + (18 – 1) d = 73


a + 17d = 73 … (2)


From (1) and (2),


a + 9d = 41


a + 17d = 73


(-) (-) (-)


-8d = -32


d = 32/8 = 4


Substituting d = 4 in (1),


a + 9(4) = 41


a = 41 – 36 = 5


Now, t27 = 5 + (27 – 1) (4)


= 5 + 26(4)


= 5 + 104


= 109


The 27th term i.e. t27 = 109


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