Algebra 2

Describe an infinite geometric series with a beginning value of 2 that converges to 10. What are the first four terms of the sequence?
a{1} = first term of series

               ∞
   Infinite Sum = ∑  a{1} • r^(n  – 1)  =  a{1}  ⁄  (1  –  r) ... for any geometric series
             n =1

  Infinite Sum for this problem = 10  =  a{1}  ⁄  (1  –  r) ... a{1} = 2 (given)

               10  =  2 ⁄ (1  –  r)

                r  =  0.8 ... common ratio

               ∞
   Infinite Sum = ∑  2 • (0.8)^(n  – 1)  ◀◀ (answer)
        n =1

   a{n} = 2 • (0.8)^(n  – 1)

   a{1} = 2 • (0.8)^(1  – 1)  =  2

   a{2} = 2 • (0.8)^(2  – 1)  =  1.6

   a{3} = 2 • (0.8)^(3  – 1)  =  1.28

   a{4} = 2 • (0.8)^(4  – 1)  =  1.024

   a{5} = 2 • (0.8)^(5  – 1)  =  0.8192

Infinite Sum = 2 + 1.6 + 1.28 + 1.024 + 0.8192 + . . . + 2  •  (0.8)^(n  – 1)  ****(answer)

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  1. is this right???

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  2. correct all the way. Good work.

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