is it possible to get a difference of 100 between any two terms of the arithmetic sequence 8,15,22...?what is the position of 351 in this sequence?
Answers
Given : arithmetic sequence 8,15,22...
To find : is it possible to get a difference of 100 between any two terms of AP
position of 351 in this sequence?
Solution:
AP is
8 , 15 , 22
a = First term = 8
d = common difference = 15 - 8 = 7
aₙ = a + ( n - 1) d
=> aₙ = 8 + (n - 1) 7
=> aₙ = 8 + 7n - 7
=> aₙ = 7n + 1
any two term of Sequence would be
7m + 1 or 7k + 1
Difference between them = 7k + 1 - (7m + 1)
= 7 (k - m)
= 7p
100 = 7 * 14 + 2
Hence it is not possible to get a difference of 100 between any two terms of the arithmetic sequence 8,15,22...
aₙ = 7n + 1
=> 351 = 7n + 1
=> 350 = 7n
=> n = 50
or 8 + (n - 1)7 = 351
=> (n - 1)7 = 343
=> n - 1 = 49
=> n = 50
Hence position of 351 is 50th
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