If 9th term of an A.P is zero, prove that its 29th term is double the 19th term.
Answers
Answer:
Given :
9th term of an AP is zero
a9 = 0
an = a + (n - 1)d
a9 = a + (9 - 1) d
0 = a + 8d
a + 8d = 0
a = - 8d ………………(1)
29 th term :
an = a + (n - 1)d
a29 = a + (29 - 1)d
a29 = a + 28d ………(2)
19 th term :
an = a + (n - 1)d
a19 = a + (19 - 1)d
a19 = a + 18d……..(3)
To prove :
a29 = 2a19
a + 28d = 2(a + 18d)
[From eq 2 & 3 ]
- 8d + 28d = 2(- 8d + 18d)
[From eq 1]
20d = 2(10d
20d = 20d
a29 = 2a19 = 20d
LHS = RHS
Hence Proved.
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Question
If 9th term of an A.P is zero, prove that its 29th term is double the 19th term.
Solution:-
Given,
9th term of A.P is zero.
a9 = 0
an = a + (n - 1) d
a9 = a + (9 - 1)d
0 = a + 8d
a + 8d = 0
a = -8d
29th term:
an = a + (n - 1) d
a29 = a + (29 - 1) d
a29 = a + 28d
19th term:
an = a + (n - 1) d
a29 = a + (19 - 1) d
a29 = a + 18d
To prove,
a29= 2a19
a + 28d = 2 (a + 18d)
[from equation 2 & 3]
-8 + 28d = 2 (-8d + 18d)
[from equation 1]
20d = 2 (10d)
20d = 20d
a29 = 2a19 = 20d
L.H.S = R.H.S
Hence, Proved.
Hope it is helpful.....