Q:

, 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

Accepted Solution

A:
Answer:The first 5 terms are -6,-25,-44,-63 and -82The sequence is arithmeticStep-by-step explanation:Given that A(n + 1) = A(n) − 19 for n ≥ 1 and A(1) = −6A(1) = -6A(2) = A(1) − 19 = -6 - 19 = -25A(3) = A(2) − 19 = -25 - 19 = -44A(4) = A(3) − 19 = -44 - 19 = -63A(5) = A(4) − 19 = -63 - 19 = -82So the first 5 terms are -6,-25,-44,-63 and -82If 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) = -19So common difference is same, so the sequence is arithmetic.