Question

Tell whether the sequence is arithmetic. If it is, identify the common difference.

1/2,1/3,1/4, ….

1) Not arithmetic
2) Arithmetic, common difference is 1/6
3) Arithmetic, common difference is 2/3
4) Arithmetic, common difference is 1

Answer 1

Not arithmetic

Explanation:

the difference of successive terms in arithmetic sequences should be the same. notice that:

1/3-1/2 =/= 1/3 - 1/4

so it's not arithmetic.

this sequence is known as the harmonic sequence, and its sum diverges.