Is 205 a term of the sequence 8, 12 , 16, 20 ...?
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Answer:
Is 205 a term of the sequence 8, 12 , 16, 20 ...?
No, Because they had the difference of 4 in each
but 205 is not a divisible of 4.
Step-by-step explanation:
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Information given to us:
- A.P. is 8, 12 , 16, 20 ...
What we have to calculate:
- We have to find out whether 205 is a term of the given sequence or not.
Finding out common difference (d):
- ⇒12 - 8 = 4
- ⇒ 16 - 12 = 4
- ⇒ 20 - 16 = 4
- ⇒24 - 20 = 4
- ⇒ 28 - 24 = 4
- ⇒ 32 - 28 = 4
Therefore, common difference (d) is 4.
Using Formula,
- n^th term = a + (n-1) d
Where,
- n is number of terms
- a is first term
- d is common difference
Substituting the values in the given formula:
Again we have,
- Number of terms is 205
- Common difference is 4
Let us do!
- ⇒ 8 + (n - 1)4 = 205
- ⇒ 8 + (n - 1) × 4 = 205
- ⇒ 8 + 4n - 4 = 205
- ⇒ 4n + 8 = 205
Transposing the side positive sign would be negative,
- ⇒ 4n = 205 - 8
Subtracting 205 with 4,
- ⇒ 4n = 201
Now,
- ⇒ n = 201 / 4
Hence,
- 205 is not a term of the given sequence because sequence can't be fraction.
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