212k views
1 vote
The 3rd and sixth terms of a G.P. are respectively 14 and 112. Find the sum of the first 10 terms of the progression.

User SubSevn
by
7.3k points

1 Answer

2 votes

Final answer:

To find the sum of the first 10 terms of a G.P., we need to determine the first term and the common ratio. Use the given values of the 3rd and 6th terms to form equations and solve for a and r. Then, use the sum formula for a G.P. to find the sum of the first 10 terms.

Step-by-step explanation:

To find the sum of the first 10 terms of a geometric progression (G.P.), we need to determine the first term (a) and the common ratio (r). Given that the 3rd term is 14 and the 6th term is 112, we can use these values to form two equations:

a * r^2 = 14

a * r^5 = 112

We can then solve these equations to find the values of a and r. Once we have the values, we can use the sum formula for a G.P. to find the sum of the first 10 terms: S = a * (1 - r^10) / (1 - r).

User Michael Shmalko
by
8.9k points