Three numbers are in arithmetic progression. The sum of the three numbers is 30 and the sum of their squares is 398. What are the three numbers?

b) An arithmetic series is such that its first term is a and its third term is b. The sum of the first n terms is Sn . Find S4 in terms of a and b. Given that S4, S5 , S7 are consecutive terms of a geometric series, show that 7a^2=13b^2 .

c) Given that the roots of the equation 3x^3 - 7x + px + 24=0 are in geometric progression, find the value of p and solve the equation.

... by step solutions to all the problems are provided. ... This is a arithmetic series with first term 2 and ... Solution: This is a geometric series whose first term a1 ...

... work, you will not receive full credit for the problem. ... the formula for the sum of an arithmetic series, what is ... 2) Use the geometric sequence of numbers 1, 3 ...

... The answer to this problem is (4 0) + (4 1) + (4 2) + (4 ... This is a geometric series (which means it is multiplicative, unlike an arithmetic series, which is ...

... Three problems with several sub categories on arithmetic sequence, geometric sequence and ... understand the technique to solve similar problems in the ...

... the horizontal represent in the context of this problem? ... of the first fifty terms of the arithmetic sequence. ... 32) Find the sum of the infinite geometric series. ...

... mean returns are NOT equal because arithmetic mean is ... of n numbers." In this regard, geometric mean is ... a 95% confidence interval, the margin of error is twice ...

... Solutions to the given problems use present value ... for ordinary annuity, annuity with geometric progression and annuity with arithmetic progression to find ...

...PROBLEM # 7 (12 points ... or decrease in cash receipts or disbursements; the arithmetic G gradient ... increase or decrease from period to period; the geometric gradient ...

... remainders, we can simplify the problem by computing ... use the properties of modular arithmetic to compute ... formula for the infinite geometric series, we obtain 1 ...