Find five numbers in G.P., such that their product is 32 and the product of the last two is 108.
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The continued product of three numbers in G.P. is 27, and the sum of theeir products in pairs is 39. Find the numbers.
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Three numbers whose sum is 18 are in A.P.; if 2,4,11 are added to them respectively, the resulting numbers are in G.P. Determine the numbers.
The sum of four numbers in G.P. is 60 and the A.M. of the first and last is 18. Find the numbers.
There are four numbers, the first three are in A.P. and the last three in G.P., the sum of the first and the last is 11, and the sum of the other two is 10, find the numbers.
The sum of the first three terms of the two series, one an A.P. and the other a G.P. is the same. If the first term of each of these is 2/3 and the common difference of the A.P. is equal to the common ratio of the G.P., find the sum of each series to 20 terms.
The sum of four numbers is GP. Is 60 and the A.M. between the first and the last is 18. Show that the numbers are 4,8,16,32.
The sum of three numbers in G.P. is 70, if the two extreme items are multiplied each by 4 and the mean by 5, the products are in A.P. Show that the numbers are 10, 20, 40.
If a, b, c are in A.P. and a, x, b and b, y, c are in G.P., show that x2, b2, y2 are in A.P.
If a, b, c are three unequal numbers in A.P. and a, b-a, c-a are in G.P., show that a/1 = b/3 = c/5