Find the number of terms of a geometric progression .find the number of terms of the series 2+6+10+14+18...that will give a sum of 800
That is not a geometric but an arithmetic sequence.
See
https://www.mathsisfun.com/algebra/sequences-sums-arithmetic.html
a = 2
d = 4
To find the number of terms in a geometric progression, you need to know the first term (a), the common ratio (r), and the sum of the series.
In this case, the first term (a) is 2 and the common ratio (r) is 4 (the difference between each term is 4).
To find the number of terms, you can use the formula for the sum of a geometric series:
Sn = a * (r^n - 1) / (r - 1)
Where Sn is the sum of the series, n is the number of terms, a is the first term, and r is the common ratio.
We want the sum of the series to be 800, so we can substitute these values into the formula:
800 = 2 * (4^n - 1) / (4 - 1)
Now, we can solve this equation to find the value of n. Let's go step by step:
1. Multiply both sides of the equation by (4 - 1) to eliminate the denominator:
800 * (4 - 1) = 2 * (4^n - 1)
2. Simplify:
2400 = 2 * (4^n - 1)
3. Divide both sides of the equation by 2 to isolate (4^n - 1):
1200 = 4^n - 1
4. Add 1 to both sides of the equation:
1200 + 1 = 4^n
5. Simplify:
1201 = 4^n
To solve for n, we need to take the logarithm of both sides of the equation using base 4:
log₄(1201) = log₄(4^n)
Using logarithm properties, we can bring down the exponent n:
n = log₄(1201) / log₄(4)
Using a calculator, calculate the logarithms:
n ≈ 5.6
Since the number of terms must be a whole number, we round up to the nearest whole number:
n = 6
Therefore, the number of terms of the series 2+6+10+14+18... that will give a sum of 800 is 6.