SOLUTION: Please help me solve this math problem:If the 10th term of a G.P is given 2^10 and the 20th term is given as 2^19.Find the first term, common ratio and the sum of the nth term

Algebra ->  Sequences-and-series -> SOLUTION: Please help me solve this math problem:If the 10th term of a G.P is given 2^10 and the 20th term is given as 2^19.Find the first term, common ratio and the sum of the nth term       Log On


   

Question 1190303: Please help me solve this math problem:If the 10th term of a G.P is given 2^10 and the 20th term is given as 2^19.Find the first term, common ratio and the sum of the nth term
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

general formula for nth term:
a%5Bn%5D=a%2Ar%5E%28n-1%29

if 10th term of a G.P is 2%5E10, we have

2%5E10=a%2Ar%5E%2810-1%29
2%5E10=a%2Ar%5E9
a=2%5E10%2Fr%5E9............eq.1


if the 20th term is given as 2%5E19, we have

2%5E19=a%2Ar%5E%2820-1%29
a=2%5E19%2Fr%5E19.........eq.2

from eq.1 and eq.2 we have

2%5E10%2Fr%5E9=2%5E19%2Fr%5E19.....solve for+r
r%5E19%2Fr%5E9=2%5E19%2F2%5E10
r%5E10=2%5E9
r+=+2%5E%289%2F10%29

then
a=2%5E10%2Fr%5E9............eq.1, substitute+r
a=2%5E10%2F%282%5E%289%2F10%29%29%5E9
a=2%5E10%2F2%5E%2881%2F10%29
a=2%2A+2%5E%289%2F10%29

so,
first term is a+=+2%2A2%5E%289%2F10%29 and common ratio is r+=+2%5E%289%2F10%29

your nth term formula is:

a%5Bn%5D=+2%2A2%5E%289%2F10%29%2A%28+2%5E%289%2F10%29%29%5E%28n-1%29