What is the sum of the first 5 terms of the geometric series 1,23,49 ...?
Answer:
21181
- The sum of first n terms of a G.P. is given by,
Sn=a(1−rn)(1−r)
Here, the first term, a=1 and
the common ratio, r=ak+1ak where k≥1
⟹r=231=23 - The sum of first n terms of this G.P. is given by,
Sn=(1)(1−(23)n)1−23=(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[1−32243]=3×211243=21181 - Hence, the sum of the first 5 terms of the G.P. is 21181.