What is the sum of the geometric sequence 2, 10, 50, … if there are 8 terms?

Answer 1

#195312#

Since the sequence is geometric, there is a constant ratio given by #r=x_(n+1)/x_n=10/2=50/10=5#
The first term is #a=2#.

The formula for the sum to n terms of such a geometric series is given by :

#sum_(k=1)^n ar^(k-1)=(a(1-r^n))/(1-r)#

So in this particular case it becomes

#sum_(n=1)^8 2*(5)^(n-1)=(2(1-5^8))/(1-5)=195312#.
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Answer 2

The sum of a geometric sequence can be calculated using the formula:

[ S_n = a \frac{{r^n - 1}}{{r - 1}} ]

Where:

  • ( S_n ) is the sum of the first ( n ) terms
  • ( a ) is the first term of the sequence
  • ( r ) is the common ratio
  • ( n ) is the number of terms

Given the sequence 2, 10, 50, ..., we can observe that:

  • ( a = 2 ) (the first term)
  • ( r = 5 ) (each term is obtained by multiplying the previous term by 5)

Now, we can plug these values into the formula:

[ S_8 = 2 \frac{{5^8 - 1}}{{5 - 1}} ]

[ S_8 = 2 \frac{{390625 - 1}}{{4}} ]

[ S_8 = 2 \frac{{390624}}{{4}} ]

[ S_8 = 2 \times 97656 ]

[ S_8 = 195312 ]

So, the sum of the geometric sequence 2, 10, 50, ... with 8 terms is 195312.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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