Question

Is 205 a term of the sequence 8,12,16,20,.......?

Answer 1

Answer:

205 = 8 + (n-1)4

198 = (n-1)4

49.5=n-1

50.5 = n

decimal term is not exist in sequence

so 205 is not lie in this sequence

Answer 2

Answer:

205 is not a term of the sequence 8,12,16,20,.....

Step-by-step explanation:

Solution:

first of all show that the given sequence is an A.P. For this:

12-8=4 , 16-12=4 , 20-16=4,....

=> difference between consecutive terms is same

=> the given sequence is an A.P.

now, let nth term of the given A.P. = 205

=> a + (n - 1)d = 205

=> 8 + (n - 1) × 4 = 205. i.e. 8 + 4n - 4 = 205

=> 4n = 205 - 4 i.e. 4n = 201

=> n = 201/4. = 50 1/4

but the number of terms in any sequence is never in fraction.

=> 205 is not a term of the sequence 8,12,16,20,.....

REMEMBER : The number of terms in every sequence is always a natural number.