Scholmo reads 7 pages of his book on the first day and his rate of reading then goes up by 3 pages each day.

a) How many pages will he have read on the 8th day?
b) After how many days will he have read more than 425 pages?

a = 7

d = 3

Now you can answer the questions:

T8 = a+7d

Sn = n/2 (2*7 + (n-1)*3) > 425

To find the number of pages Scholmo will have read on the 8th day, we need to determine the pattern of his reading rate. We know that he reads 7 pages on the first day and his rate of reading increases by 3 pages each day.

a) To find the number of pages Scholmo will have read on the 8th day, we can use the formula for the sum of an arithmetic series:
Sn = (n/2)(2a + (n-1)d),
where Sn is the sum of the series, n is the number of terms, a is the first term, and d is the common difference.

In this case, the number of terms, n, is 8 (since we want to find the number of pages on the 8th day), the first term, a, is 7 (the number of pages he read on the first day), and the common difference, d, is 3 (the increase in the number of pages each day).

Plugging these values into the formula, we have:
S8 = (8/2)(2*7 + (8-1)*3),
S8 = 4(14 + 7*3),
S8 = 4(14 + 21),
S8 = 4(35),
S8 = 140.

Therefore, Scholmo will have read 140 pages on the 8th day.

b) To find the number of days it will take for Scholmo to read more than 425 pages, we can set up an equation based on the information given.

Let n be the number of days it takes for Scholmo to read more than 425 pages. We know that his reading rate increases by 3 pages each day, so we can use the formula for the sum of an arithmetic series to calculate the total number of pages he will have read after n days:

Sn = (n/2)(2a + (n-1)d),

Using the values we have, Sn > 425, a = 7, and d = 3, we can rewrite the equation as:

(n/2)(2*7 + (n-1)*3) > 425.

Simplifying the equation:

(n/2)(14 + 3n - 3) > 425,
(n/2)(11 + 3n) > 425.

Expanding the brackets:

(11n + 3n^2)/2 > 425.

Now we can multiply both sides of the inequality by 2 to get rid of the fraction:

11n + 3n^2 > 850.

Rearranging the equation to find n:

3n^2 + 11n - 850 > 0.

To solve the quadratic inequality, we can factor or use the quadratic formula. Factoring is not feasible in this case, so we will use the quadratic formula:

n = (-b ± √(b^2 - 4ac))/(2a).

For this equation, a = 3, b = 11, and c = -850. Plugging these values into the quadratic formula, we get:

n = (-11 ± √(11^2 - 4*3*(-850)))/(2*3),
n = (-11 ± √(121 + 10200))/6,
n = (-11 ± √10321)/6.

Calculating the square root:

n = (-11 ± 101.6)/6.

Using both the positive and negative values:

n = (-11 + 101.6)/6 and n = (-11 - 101.6)/6.

Simplifying each equation:

n = 90.6/6 and n = -112.6/6,
n ≈ 15.1 and n ≈ -18.8.

Since the number of days cannot be negative, we discard n ≈ -18.8 as it is not a valid solution.

Therefore, it will take Scholmo approximately 15.1 days to read more than 425 pages. However, since the number of days must be a whole number, we can conclude that it will take him 16 days to read more than 425 pages.