Question

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

Answer 1

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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Answer 2

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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