If the 9th term of an ap is 0 prove that its 29th term is twice the 19th term
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so the given equation is proved and verified
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Question:-
➡ If the 9th term of an A.P. is zero then prove that, 29th term is twice the 19th term.
Proof:-
Let us assume that,
➡ First term of the A.P. = a and,
➡ Common Difference = d
Now,
Nth term of an A.P. = a + (n -1)d
So,
9th term = a + (9 - 1)d
= a + 8d
Now, it's given that, 9th term of the A.P. is zero.
➡ a + 8d = 0 .....(i)
Now,
29th term = a + (29 - 1)d
= a + 28d
19th term = a + (19 - 1)d
= a + 18d
Now,
29th term - 2 × 19th term
= a + 28d - 2 × (a + 18d)
= a + 28d - 2a - 36d
= -a - 8d
= -1(a + 8d)
= -1 × 0
= 0
Hence,
29th term - 2 × 19th term = 0
➡ 29th term = 2 × 19th term. (Hence Proved)
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