If (2k+1),(4k+3) and (8k+1) are three consecutive terms of an AP.Find the value of k and 18th term of the sequence.
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Given : (2k+1),(4k+3) and (8k+1) are three consecutive terms of an AP
To Find : value of k
Solution:
(2k+1),(4k+3) and (8k+1) are three consecutive terms of an AP
=> (2k + 1) + (8k + 1) = 2(4k + 3)
=> 2k + 1 + 8k + 1 = 8k + 6
=> 2k + 2 = 6
=> 2k = 4
=> k = 2
Value of k = 2
As we do not know 1st term we can not find 18 th term
Assuming (2k+1),(4k+3) and (8k+1) are first three terms
Then 5 , 11 , 17
a = 5
d = 6
18th term = 5 + ( 18 - 1) * 6
= 5 + 17 * 6
= 5 + 102
= 107
18th term = 107
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