Question

If 11 times of 11th term is equal to 17 times of 17th term of an A.P. find its 28th term

Answer 1

hope u get the solution

Answer 2

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$\tiny n$ = 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 = $\frac{ - 162 }{6}$ .

=> 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 ✅✅.

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#BeBrainly.