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Oduvanchick [21]
3 years ago
5

Write each sum using summation notation 12 + 22 + 32 + 42 + ⋯ + 10000^2

Mathematics
1 answer:
Murljashka [212]3 years ago
5 0

Answer:

50,00,70,000

Step-by-step explanation:

The given sequence is Arithmetic Progression.

Arithmetic Progression is a sequence in which every two neighbor digits have equal distances.

Here first we will find the number of terms

For finding the nth term, we use formula

aₙ = a + (n - 1) d

where, aₙ = value of nth term

a = First term

n = number of term

d = difference

Now, In given sequence: 12, 22, 32, 42, ⋯ , 100002

a = 12, d = 10, n = ? and  aₙ= 100002

∴ 100002  = 12 + (n - 1) × (10)

⇒ 99990 = 10(n - 1)

⇒ n = 10000

Now using the formula of Sum of Arithmetic Sequence,

Sₙ = n÷2[2a + (n - 1)d]

⇒ Sₙ = (10000÷2)[2 × 12 + 9999 × 10]

⇒ Sₙ = 5000 [ 24 + 99990]

⇒ Sₙ = 5000 × 100014 = 50,00,70,000

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A nature museum has 2008 specimens of early birds, some with 222 wings and some with 444 wings. The specimens have a total of 40
ludmilkaskok [199]

Let's assume

number of birds with 2 wings is x

number of birds with 4 wings is y

A nature museum has 2008 specimens of early birds

so,

x+y=2008

Total of wings of 2 wings bird =2x

Total of wings of 4 wings bird =4y

The specimens have a total of 4384 wings

so, we get

2x+4y=4384

we can divide both sides by 2

x+2y=2192

so, we get system of equations as

x+y=2008

x+2y=2192

we can solve for x and y

We can subtract both equations

2008-y+2y=2192

y=184

x=2008-184

x=1824

y=184,\:x=1824

so,

number of birds with 2 wings is 1824

number of birds with 4 wings is 184.............Answer



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