find the common difference of an AP whose 1st term is 100 and the sum of whose first six terms is 5 times the sum of the next 6 terms?

find the common difference of an AP whose 1st term is 100 and the sum of whose first six terms is 5 times the sum of the next 6 terms?

unknown values: d

equation: m = 100 + 5*d

equation: n = 100 + 6*d

equation: k = 100 + 11*d

equation: (100 + m) * 6 / 2 = 5 * (n + k) * 6 / 2

answer: -10

If (a+b)/a=6 and (b+c)/c=9 then what is the numerical value of a/c?

unknown values: a/c

equation: (a+b)/a=6

equation: (b+c)/c=9

answer: 8/5 | 1.6

Find The sum of all integer multiples of 7 from 7 to 700

unknown values: s

equation: s = (7+700)*((700-7)/7+1)/2

answer: 35350

Searching for the value of a variable in a fraction?15/630,000 = 0.50/b

unknown values: b

equation: 15/630000 = 0.50/b

answer: 21000

nine times the reciprocal of a number equals 3 times the reciprocal of 4?Find the number.

unknown values: n

equation: 9/n = 3/4

answer: 12

Two times the reciprocal of a number equals 28 times the reciprocal of 35. Find the number.

unknown values: n

equation: 2/n = 28/35

answer: 5/2 | 2.5

If 2/3 is 1/2 of 4/5 of a certain number, then that number is what?

unknown values: n

equation: 2/3 = 1/2 * 4/5 * n

answer: 5/3

A number is 5 less than the square of the other number. The product of the two numbers is 12. What are the numbers?

unknown values: x,y

equation: x = y^2 - 5

equation: xy = 12

answer: {4; 3}

In an arithmetic sequence, the 7th term minus the 1st term equals 18. The sum of the 1st and 7th term is -2. Find the 6th term.

unknown values: x

equation: a + (7-1)*d - a = 18

equation: a + (7-1)*d + a = -2

equation: x = a + (6-1)*d

answer: 5

if the product of (2+3), (3+4), and (4+5) is equal to the sum of 40 and x then x=?

unknown values: x

equation: (2+3)(3+4)(4+5) = 40 + x

answer: 275