The, 8th sum of a gp is 640 if the first term is5 find the common ratio and 10th term solve
5(r^8 - 1)/(r-1) = 640
Use that to find r, and then 5r^9
Not what I expected for r. Is there maybe a typo?
The 8th term of a g.p is 640, if the first term a is 5. Find (a)the common different r (b)the term term
To solve this problem, we'll use the formula for the sum of a geometric progression (GP):
Sn = a * (r^n - 1) / (r - 1)
where:
- Sn is the sum of the first n terms of the GP
- a is the first term
- r is the common ratio
- n is the number of terms
We are given that the 8th sum of the GP is 640 and the first term is 5. Substituting these values into the formula, we get:
640 = 5 * (r^8 - 1) / (r - 1)
To find the common ratio (r), we'll rearrange the equation and solve it.
Step 1: Multiply both sides of the equation by (r - 1) to remove the denominator:
640 * (r - 1) = 5 * (r^8 - 1)
Step 2: Expand the brackets:
640r - 640 = 5r^8 - 5
Step 3: Bring all terms to one side:
5r^8 - 640r + 5 - 640 = 0
Step 4: Simplify the equation:
5r^8 - 640r - 635 = 0
We have now obtained the equation 5r^8 - 640r - 635 = 0.
To solve this equation and find the value of r, we can use numerical methods like the Newton-Raphson method, but it involves complex calculations. Therefore, I recommend solving this equation using a computer algebra system such as Wolfram Alpha or using a graphing calculator.