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ch4aika
8 days ago
8

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

Mathematics
1 answer:
lawyer [12.5K]8 days ago
6 0

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

By subtracting one equation from the other

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

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

5d = 25

d = 25/5

d = 5

Now replace d in either equation to solve for 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

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