algebra

The fourth term of a G. P. is 216 and the \(6^{th}\) term is 1944. Find the \(8^{th}\) term.

Determine x so that: x, \(2x+7\), \(10x-7\) will be a geometric progression.

If one third of the air in a tank is removed by each stroke of an air pump, what fractional part of the total air is removed in 6 strokes?

A product has a current selling of P 325.00. If its selling price is expected to decline at the rate of \(10\%\) per annum because of obsolescence, what will be its selling price four years hence?

The numbers 28, \(x+2\), 112 form a G. P. What is the \(10^{th}\) term?

The seventh term is 56 and the twelfth term is -1792 of a geometric progression. Find the common ratio and the first term. Assume the ratios are equal.

A person has 2 parents, 4 grandparents, 8 great grandparents and so on. How many ancestors during the 15 generations preceding his own, assuming no duplication?

In the PBA three-point shootout contest, the committee decided to give a prize in the following manner: A prize of P1 for the first basket made, P 2 for the second, P 4 for the third, P8 for the fourth and so on. If the contestant wants to win a prize of no less than a million pesos, what is the minimum number of baskets to be converted?

In a benefit show, a number of wealthy men agreed that the first one to arrive would pay 10 centavos to enter and each later arrive would pay twice as much as the preceding man. The total amount collected from all of them was P 104,857.50. How many wealthy men paid?

A man mailed 10 chain letters to ten of his friends with a request to continue by sending a similar letter to each of their ten friends. If this continue for 6 sets of letters and if all responded, how much will the Phil. Postal office earn if minimum postage costs P 4 per letter?

Under favorable condition, a single cell bacteria divided into two about every 20 minutes. If the same rate of division is maintained for 10 hours, how many organisms is produced from a single cell?

A rubber ball is made to fall from a height of 50 feet and is observed to rebound \(2/3\) of the distance it falls. How far will the ball travel before coming to rest if the ball continues to fall in this manner?

In the series 1, 1, \(1/2\), \(1/6\), \(1/24\),..., determine the \(6^{th}\) term.

Find the \(1987^{th}\) digit in the decimal equivalent to \(\frac{1785}{9999}\) starting from the decimal point.

A man rows upstream and back in 12 hours. If the rate of the current is 1.5 kph and that of the man in still water is 4 kph, what was the time spent downstream?

The first term of a GP is 160 and the common ratio is 3/2. How many consecutive terms must be taken to give a sum of 2,110?

How many arrangements of the letters in the word “VOLTAGE” begin with a vowel and end with a consonant?

The plate number of a vehicle consists of 5 alphanumeric characters such that the first 2 characters are letters and the remaining 3 are digits. How many arrangements are possible if the first character is a vowel and repetition is not allowed?

A sports car 2 m long overtakes a 12 m van which is traveling at the rate of 36 kph. How fast must the car travel to overtake the van in 3 seconds if their rear ends are aligned initially?

By stringing together 9 differently colored beads, how many different bracelets can be made?