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3 years ago

Find the sixth term of the sequence 1/2, -3/8, 9/32

Mathematics

2 answers:

sukhopar [10]3 years ago

8 0

Answer:

The sixth term is -243/2048 ⇒ answer B

Step-by-step explanation:

* Lets explain the geometric sequence

- There is a constant ratio between each two consecutive numbers

- Ex:

# 5 , 10 , 20 , 40 , 80 , ………………………. (×2)

# 5000 , 1000 , 200 , 40 , …………………………(÷5)

* General term (nth term) of a Geometric sequence:

# U1 = a , U2 = ar , U3 = ar² , U4 = ar³ , U5 = ar^4

# Un = ar^(n-1), where a is the first term , r is the constant ratio

between each two consecutive terms and n is the position of the

number in the sequence

- Ex: U5 = ar^4 , U7 = ar^6 , U10 = ar^9 , U12 = ar^11

- Lets solve the problem

∵ The sequence is 1/2 , -3/8 , 9/32

- Lets find the constant ratio r

∵ The first term is a = 1/2

∵ The second term is U2 = ar

∵ The second term U2 = -3/8

∴ ar = -3/8

∴ 1/2 r = -3/8 ⇒ multiply both sides by 2

∴ r = -3/4

- Lets find the sixth term

∵ a = 1/2 and r = -3/4

∵ n = 6

∴ U6 = ar^5

∴ U6 = 1/2 (-3/4)^5 = 1/2 × -243/1024 = -243/2048

* The sixth term is -243/2048

Umnica [9.8K]3 years ago

8 0

Answer:

B edge

Step-by-step explanation:

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