Question

arithmetic sequences quiz

1. find the equation (no spaces!): -2, 3, 8, 13, ....

t(n) =

n +

1. find the equation (no spaces!): 1, -3, -7, -11, ...

t(n) =

n +

Explanation:

Question 1

Step1: Identify common difference (d)

The sequence is -2, 3, 8, 13, ... . To find \( d \), subtract consecutive terms: \( 3 - (-2) = 5 \), \( 8 - 3 = 5 \), \( 13 - 8 = 5 \). So \( d = 5 \).

Step2: Use arithmetic sequence formula \( t(n) = a_1 + (n - 1)d \)

First term \( a_1 = -2 \), \( d = 5 \). Expand the formula: \( t(n) = -2 + (n - 1) \times 5 \). Simplify: \( t(n) = -2 + 5n - 5 = 5n - 7 \).

Step1: Identify common difference (d)

The sequence is 1, -3, -7, -11, ... . Subtract consecutive terms: \( -3 - 1 = -4 \), \( -7 - (-3) = -4 \), \( -11 - (-7) = -4 \). So \( d = -4 \).

Step2: Use arithmetic sequence formula \( t(n) = a_1 + (n - 1)d \)

First term \( a_1 = 1 \), \( d = -4 \). Expand: \( t(n) = 1 + (n - 1) \times (-4) \). Simplify: \( t(n) = 1 - 4n + 4 = -4n + 5 \).

Answer:

\( t(n)=5n+-7 \)

Question 2