Question

if 7 times and 7th term of an ap is equal to 11th term.show that it's 18th term is 0

Answer 1

Heyy mate ❤✌✌❤

Here's your Answer...

7( a7) = a11

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

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

=> 4a - 68d =0

=> a = 68d/4

=> a = 17d.------(1)

Now, a18 = a + 17d ------(2)

From eq 1 and 2.

a18 =0.
✔✔✔

Answer 2

7th term = (a+6d)                         11th term = (a+10d)
(a+6d)7  since 7th term of the ap is 7 times               and the same for 11th term
(a+6d)7=(A+10d)11                   (given)
7a + 42d =11a +110d                       (on solving)
7a - 11a = 110d - 42d
-4a = -68d
a= -17d


we know 18th term = (a+17d)................................. (i)
now we substitute the value of a in (i) 
which emplies,
                       +17d -17d

=0