Question

, list the first five terms of each sequence, and identify them as arithmetic or geometric.

A(n + 1) = A(n) − 19 for n ≥ 1 and A(1) = −6

Answer 1

The first 5 terms are -6,-25,-44,-63 and -82

The sequence is arithmetic

Explanation:

Given that A(n + 1) = A(n) − 19 for n ≥ 1 and A(1) = −6

A(1) = -6

A(2) = A(1) − 19 = -6 - 19 = -25

A(3) = A(2) − 19 = -25 - 19 = -44

A(4) = A(3) − 19 = -44 - 19 = -63

A(5) = A(4) − 19 = -63 - 19 = -82

So the first 5 terms are -6,-25,-44,-63 and -82

If they are in arithmetic the common difference will be same, if geometric common ratio will be same.

Let us check common difference,

-25-(-6) = -19

-44-(-25) = -19

-63-(-44) = -19

-82-(-63) = -19

So common difference is same, so the sequence is arithmetic.