Step-by-step explanation:
1. if the number of pages in the 1st day is 'x', then the 2d day - 'x+10', the 3d day - 'x+20', the 4th day - 'x+30', the 5th day - 'x+40' and the last day - 'x+50' pages;
2. if the sum of all the pages is 300, then it is possible to make up the equation:
x+x+10+x+20+x+30+x+40+x+50=300;
3. x=25, it means:
1st day - 25;
2d day - 35;
3d day - 45;
4th day - 55;
5th day - 65;
6th day - 75 pages.
a = 4 first term, r = ?, T10 = 100.
Tn = ar^n - 1 formula for g.p
T10 = 4r^ 10 - 1
100 = 4r^9
Divide both side by 4
100/4 = 4/4r^9
25 = r^9 take the 9th root of both side
9√25 = 9√r^9
r = 9√25
To find the nth term
Since Tn = ar^n - 1
Let's call our estimate x. It will be the average of n IQ scores. Our average won't usually exactly equal the mean 97. But if we repeated averages over different sets of tests, the mean of our estimate the average would be the same as the mean of a single test,
μ = 97
Variances add, so the standard deviations add in quadrature, like the Pythagorean Theorem in n dimensions. This means the standard deviation of the average x is
σ = 17/√n
We want to be 95% certain
97 - 5 ≤ x ≤ 97 + 5
By the 68-95-99.7 rule, 95% certain means within two standard deviations. That means we're 95% sure that
μ - 2σ ≤ x ≤ μ + 2σ
Comparing to what we want, that's means we have to solve
2σ = 5
2 (17/√n) = 5
√n = 2 (17/5)
n = (34/5)² = 46.24
We better round up.
Answer: We need a sample size of 47 to be 95% certain of being within 5 points of the mean
