Question

The 8th term of an AP is zero. Prove that it's 38th term is triple it's 18th tern

Answer 1

$\textbf{Heya}$

$\textbf{Given:-}$

a8 = 0

To prove :- a38 = 3(a18)

Proof:-

Using formula

an = a + (n - 1)d
a8 = a + 7d = 0 ............(1)

a38 = a + 37d
a38 = a + 7d + 30d
a38 = 0 + 30d ...........(using eq (1))
a38 = 30d ..........(2)

Now,
a18 = a + 17d
a18 = a + 7d + 10d
a18 = 0 + 10d ...........(using eq (1))
a18 = 10d ............(3)

We can also write eq (2) as

a38 = 30d
a38 = 3(10d)
a38 = 3(a18) .............(using eq(3))

Hence proved

$\textbf{Hope \ this \ helps \ you }$

Answer 2

Hey !!



8th term = 0


a + 7d = 0


a = -7d



To prove :-


38th term = 3 ( 18th term )



a + 37d = 3 ( a + 17d )


-7d + 37d = 3 ( -7d + 17d )



30d = 3 ( 10d)

30d = 30d.


LHS = RHS .