Question

Indicate the general rule for the arithmetic sequence with a3 = 8 and a8 = 33.

Answer 1

Answer:

$u_{n} = -2 + (n-1)5$

Step-by-step explanation:

$u_{n} = a + (n-1)d$

$u_{3} = a + (3-1)d = 8$

$u_{3} = a + 2d = 8$

$u_{8} = a + (8-1)d = 33$

$u_{8} = a + 7d = 33$

Simultaenous Equations

a + 2d = 8

a + 7d = 33

Subtract the equations

(a + 7d = 33) - (a + 2d = 8)

(a - a) + (7d - 2d) = (33 - 8)

5d = 25

d = 25/5

d = 5

Subsitute d into either equation to find a

a + 2(5) = 8

a + 10 = 8

a = 8 - 10 = -2

a = -2

a + 7(5) = 33

a + 35 = 33

a = 33 - 35 = -2

a = -2

$u_{n} = -2 + (n-1)5$