Find the sum of 33 terms of an arithmetic progression whose middle term is 33.

Find the sum of 33 terms of an arithmetic progression whose middle term is 33.

unknown values: s

equation: a + (33-1)*d = b

equation: s = (a+b)*33/2

equation: a + ((33+1)/2-1)*d = 33

answer: 1089

The first 3 terms of a geometric series sum to -189, and the next 3 terms sum to 7. What is the sum of the first 2 terms of the series?

unknown values: s

equation: a + aq + a*q^2 = -189

equation: a*q^3 + a*q^4 + a*q^5 = 7

equation: s = a + aq

answer: -162

Seven more than the product of a number and four is negative seventeen. find the number.

unknown values: n

equation: 7 + 4*n = -17

answer: -6

The sum of two numbers is 28. Their products is 7.Find the sum of the reciprocals of the numbers!

unknown values: m

equation: x + y = 28

equation: x * y = 7

equation: m = 1/x + 1/y

answer: 4

How many 7-digit telephone numbers are there if the number meets the following conditions?- the first digit is not 5 or 7- the second digit is 7- the fifth digit is 1- the last digit is 3- none of the digits is 6- the leading digit may not be 0 or 1

unknown values: n

equation: n = 5 * 1 * 9 * 9 * 1 * 9 * 1

answer: 3645

find four consecutive odd integers such that 6 times the sum of the first and the third is 3 more than 5 times the opposite of the fourth.

unknown values: 2*n-3,2*n-1,2*n+1,2*n+3

equation: 6((2*n-3) + (2*n+1)) = 3 + 5(-1 * (2*n+3))

answer: -3; -1; 1; 3

what is the sum of all the four digit positive integers that can be written with the digits 1, 2, 3, and 4 if each digit must be used exactly once in each four digit positive integer.

unknown values: s

equation: s = (1+2+3+4)*(3*2)*(1000+100+10+1)

answer: 66660

If you subtract a number from four times its square, the result is three? Find the number.

unknown values: n

equation: 4*n^2-n=3

answer: 1 or -3/4 | 1 or -0.75

The sum of the first 100 positive whole numbers is 5050. what is the sum of the first 100 positive odd whole numbers ?

unknown values: s

equation: s = 2 * 5050 - 100 * 1

answer: 10000

Jabari is thinking of three numbers. The greatest number is twice as big as the least number. The middle number is three more than the least number. The sum of the three numbers is 75. Find the numbers.

unknown values: x,y,z

equation: x = 2*z

equation: y = 3 + z

equation: x + y + z = 75

answer: {36; 21; 18}