Question

1. what are the first five terms in the recursive sequence defined by the following?

$a_1 = 150$
$a_n = 0.85a_{n - 1}$
{0.85, 150.85, 300.85, 450.85, 600.85}
{0.15; 22.5; 3,375; 506,250; 75,937,500}
{150, 22.5, 3.375, 0.50625, 0.0759375}
{150, 127.5, 108.375, 92.11875, 78.3009375}

Explanation:

Step1: Identify first term

$a_1 = 150$

Step2: Calculate second term

$a_2 = 0.85a_1 = 0.85 \times 150 = 127.5$

Step3: Calculate third term

$a_3 = 0.85a_2 = 0.85 \times 127.5 = 108.375$

Step4: Calculate fourth term

$a_4 = 0.85a_3 = 0.85 \times 108.375 = 92.11875$

Step5: Calculate fifth term

$a_5 = 0.85a_4 = 0.85 \times 92.11875 = 78.3009375$

Answer:

{150, 127.5, 108.375, 92.11875, 78.3009375} (the fourth option)