Question

in an ap the 7 times the 7 term is equal to 11times the 11terms find the 18 term of an ap

Answer 1

hi!!

Let the first term of AP be a and common difference be d.

Since a(n) th term = a + (n-1)d

=) 7th term = a + (7-1)d

= a + 6d

Similarly 11th term = a + 10d

A/Q;

=) 7(a + 6d) = 11(a +10d)

=) 7a + 42d = 11a + 110d

=) 7a - 11a = 110d - 42d

=) - 4a = 68d

=) a = 68d/-4

=) a = - 17d

To find 18th term;

=) 18th term = a + (18-1)d

= - 17d + 17d

= 0

Hope it helps uh!!

Answer 2

Hey there !!


➡ Given :-

→ 7 times the 7th term = 11 times the 11th term [ 7a$\tiny 7$ = 11a$\tiny 11$ . ]



➡ To find :-

→ 18th term [ a$\tiny 18$ ].


➡ Solution :-

▶ Let a be the first term and d be the common difference of the AP.

▶ Do, nth term is given by :-

→ a$\tiny n$ = a + ( n - 1 )d.

→ Then, 7th term [ a$\tiny 7$ ] = a + 6d.

And, 11th term [ a$\tiny 11$ ] = a + 10d.

▶ Now,

We have ,

→ 7a$\tiny 7$ = 11a$\tiny 11$ .

=> 7 ( a + 6d ) = 11 ( a + 10d ).

=> 7a + 42d = 11a + 110d.

=> 11a - 7a = 42d - 110d.

=> 4a = - 68d.

=> a = $\frac{ - 68d}{4}$ .

=> a = - 17d.


▶ Then, 18th term [ a$\tiny 18$ ] is given by :-

→ a$\tiny 18$ = a + ( n - 1 )d.

=> a$\tiny 18$ = - 17d + ( 18 - 1 )d.
[ → a = -17d ].

=> a$\tiny 18$ = - 17d + 17d .

=> a$\tiny 18$ = 0.


✔✔ Hence, 18th term of the AP is equal to 0 ✅✅.

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THANKS


#BeBrainly.