an AP consists of 60 terms of which 3rd term is 7 and the last term is 178 find the 19th term
Share
an AP consists of 60 terms of which 3rd term is 7 and the last term is 178 find the 19th term
Sign Up to our social questions and Answers Engine to ask questions, answer people’s questions, and connect with other people.
Login to our social questions & Answers Engine to ask questions answer people’s questions & connect with other people.
Given :-
To find :-
Solution :-
In order to find the 19th term of AP, firstly we have to find the common difference and first term of the AP.
3rd term of AP = 7 [Given]
⇝ a3 = 7
⇝ a + 2d = 7 - - - - Eqn(1)
last term of AP = 178 [Given]
⇝ a60 = 178
⇝ a + 59d = 178 - - - - Eqn(2)
Eqn(2) - Eqn(1)
⇝ a + 59d - (a + 2d) = 178 - 7
⇝ a + 59d - a - 2d = 171
⇝ 57d = 171
⇝ d = 171 / 57
⇝ d = 3
Substitute this value of d in Eqn(1) :-
⇝ a + 2d = 7
⇝ a + 2(3) = 7
⇝ a + 6 = 7
⇝ a = 7 - 6
⇝ a = 1
Now we have formula to find nth term of AP :-
⇝ an = a + ( n - 1 ) d
Substitute value of a = 1 , d = 3 and n = 19 for 19th term
⇝ a19 = 1 + ( 19 - 1 ) ( 3 )
⇝ a19 = 1 + ( 18 ) ( 3 )
⇝ a19 = 1 + 54
⇝ a19 = 55
So the required 19th term of AP is 55.
More :-
Amswer is 53.
Thank You...