Question

Show how the following sequences is an arithmetic or not
please help me ​

Answer 1

not arithmetic

Explanation:

An arithmetic sequence has a common difference d between consecutive terms.

Given

`T_(n)` = 2n² - 1

Substitute in n = 1, 2, 3, 4 to generate the first 4 terms of the sequence

`T_(1)` = 2(1)² - 1 = 2 - 1 = 1

`T_(2)` = 2(2)² - 1 = 8 - 1 = 7

`T_(3)` = 2(3)² - 1 = 18 - 1 = 17

`T_(4)` = 2(4)² - 1 = 32 - 1 = 31

check the difference between consecutive terms

7 - 1 = 6

17 - 7 = 10

31 - 17 = 14

The differences are not common hence not an arithmetic sequence