Question

Which of the following best describes the following set of numbers? 6 + 8 + 10 + 12 + ... + (4 + 2n) + ...

answers:
Arithmetic SequenceGeometric SeriesGeometric SequenceArithmetic Series

Answer 1

The term that best describes the given set of numbers is:

Arithmetic Series.

Explanation:

We are given a series of numbers as:

6 + 8 + 10 + 12 + ... + (4 + 2n) + ...

Clearly as wee could see that each term in the given expression is separated by a plus sign, Hence, the given expression is a series and not a sequence.

Also as we could see that each in the series is more than the preceding term by 2 i.e. the common difference of the term is 2.

( Since, the set of numbers is given as:

`a_0+a_1+a_2+a_3+....`

where,

`a_n=2n+4`

`when,n=0\\\\a_1=4\\\\when,n=1\\\\a_1=6\\\\and\ so\ on`

Also,

`a_0-a_1=2\\\\Simialrly\\a_2-a_1=2\\\\and\ so\ on`

Hence, the common difference is 2. )

Hence, the given series is an Arithmetic series.

Answer 2

From the series given:
6+8+10+12+.....+(4+2n)+
the common difference is:
8-6=10-8=12-10=2
since the series has a common difference then it is known as:
Arithmetic series.