What is the sum of the first 5 terms of the geometric series 1,23,49 ...?


Answer:

21181

Step by Step Explanation:
  1. The sum of first n terms of a G.P. is given by,
    Sn=a(1rn)(1r)
    Here, the first term, a=1 and
    the common ratio, r=ak+1ak where k1
    r=231=23
  2. The sum of first n terms of this G.P. is given by,
    Sn=(1)(1(23)n)123=(1(23)n)13=3[1(23)n] Now, the sum of the first 5 terms of the G.P is given by, S5=3[1(23)5]=3[132243]=3×211243=21181
  3. Hence, the sum of the first 5 terms of the G.P. is 21181.

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