Q. 144.1( 14 Votes )

Which term of the AP 3, 8, 13, 18, ... will be 55 more than its 20th term?

Answer :

In the given AP, the first term = a = 3

Common difference = d = 8 - 3 = 5


To find: place of the term which is 55 more than its 20th term.


So, we first find its 20th term.


Since, we know that


an = a + (n - 1) × d


a20 = 3 + (20 - 1) × 5


a20 = 3 + 19 × 5


a20 = 3 + 95


a20 = 98


20th term of the AP is 98.


Now, 55 more than 20th term of the AP is 55 + 98 = 153.


So, to find: place of the term 153.


So, let an = 153


Since, we know that


an = a + (n - 1) × d


153 = 3 + (n - 1) × 5


153 - 3 = 5n - 5


150 = 5n - 5


150 + 5 = 5n


5n = 155


n = 155/5 = 31


31st term of the AP is the term which is 55 more than 20th term.


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