Lab Math Homework: HW 11.2 Arithmetic Sequences Question 10, 11.2.17 Courses surse Home Use the formula for the general term (th

Math

Sequences & Series Solutions

esc 15. There were 32 chess players in the competition. After the first round, 16 players remained. After the second round, 8 players remained. Write an equation for the nth term of the geometric sequence. How many players remained after the fifth round? 10 CO 8 3 15 2 5 7 12 4 13 9 14 1 11 6

Math

Sequences & Series Solutions

The selected statement is true because both sides of the equation equal the same quantity. Show that for each integer k 2 0, if P(k) is true, then P(k + 1) is true: Let k be any integer with k 2 0, and suppose that P(k) is true. Select the expression for the left-hand side of P(k) from the choices below. k+1 1.2k + i = 1 1 k+1 O Si. 2 i = 1 k+1 O 1.2k O i = 1 k+1 lo Iki 2 i = 1 The right-hand side of P(k) is i: 21 X. [The inductive hypothesis states that the two sides of P(k) are equal.] (k+1)+1 (k+1)+1 We must show that P(k + 1) is true. The left-hand side of Plk + 1) is I i. 2'. When the final term of ;. 2' is written i = 1 i = 1 k+1 (k+1)+1 separately, the result is 1.2i = 1.2+ . The right-hand side of Pík + 1) is . After i = 1 i = 1 substitution from the inductive hypothesis, the left-hand side of P(K + 1) becomes + (k + 2)2k + 2 2)2* + 2) When the left-hand and right-hand sides of P(K + 1) are simplified, they both can be shown to equal + 2. Hence Plk + 1) is true, which completes the inductive step.

Algebra

Sequences & Series Solutions

The height (in feet) of a punted football is a function of the time the ball is in the air. The function is defined by the equation below. What is the height of the ball after 4 seconds? h(t): = -7t² + 48 t 1. 48 feet 2. 80 feet 3. -304 feet 4. 97 feet