if the 9 term of an ap is zero then show that 29
Answers
Answer:
answer is twice 19
Step-by-step explanation:
It is given that the 9
th
term of an A.P is T
9
=0
We know that the general term of an arithmetic progression with first term a and common difference d is T
n
=a+(n−1)d, therefore, the 9
th
, 19
th
and 29
th
terms are as follows:
T
9
=a+(9−1)d=a+8d.......(1)
T
19
=a+(19−1)d=a+18d......(2)
T
29
=a+(29−1)d=a+28d.......(3)
Now since T
9
=0, therefore, equation 1 becomes
0=a+8d
⇒a=−8d........(4)
Substitute the value of equation (4) in equation (3):
T
29
=−8d+28d=20d=2(10d)=2(−8d+18d)=2(a+18d)=2[T
19
] (Using equations 1 and 2)
Hence, the 29th term of A.P is twice the 19 term.
Answer:
The term is 0.
Step-by-step explanation:
Substituting n = 9 in this formula.
20d = 2(10d). 20d = 20d.
Therefore it is proved that 29th term is twice the 19th term when the 9th term is 0.
HOPE THIS WILL HELP YOU.
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