If 11 times of 11th term is equal to 17 times of 17th term of an A.P. find its 28th term
Share
If 11 times of 11th term is equal to 17 times of 17th term of an A.P. find its 28th 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.
Hey there !!
➡ Given :-
→ 11 times the 11th term = 17 times the 17th term [ 11a₁₁ = 17a₁₇ . ]
➡ To find :-
→ 28th term [ a₂₈ ].
➡ Solution :-
▶ Let a be the first term and d be the common difference of the AP.
▶ Then, nth term is given by :-
→ a = a + ( n - 1 )d.
→ Then, 11th term [ a₁₁ ] = a + 10d.
And, 17th term [ a₁₇ ] = a + 16d.
▶ Now,
We have ,
→ 11a₁₁ = 17a₁₇ .
=> 11 ( a + 10d ) = 17 ( a + 16d ).
=> 11a + 110d = 17a + 272d.
=> 17a - 11a = 110d - 272d.
=> 6a = - 162d.
=> a = .
=> a = - 27d.
▶ Then, 28th term [ a₂₈ ] is given by :-
→ a₂₈ = a + ( n - 1 )d.
=> a₂₈ = - 27d + ( 28 - 1 )d.
[ → a = -27d ].
=> a₂₈ = - 27d + 27d .
=> a₂₈ = 0.
✔✔ Hence, 28th term of the AP is equal to 0 ✅✅.
__________________________________
THANKS
#BeBrainly.