LAST TIME REVISION GEOMETRIC PROGRESSION

1) Find the 10th term of the GP 2,6,18,54,....    39366

2) The 3rd and the 7th terms of a GP are 4 and 64 respectively. Find the GP.     

3) Find the sum of the following geometric series:
a)  3-9+ 27- 81 +....8 terms.            -4920

4) 1 + 1/4+ 1/16+ 1/64+....10 terms.      4/3(1- 1/4¹⁰)

5) The sum of first 6 terms of a GP is 9 times the sum of its first 3 terms. Find the common ratio of the GP.      2

6) The mth terms of a GP is n and nth term is m. Find its (2m - n)th term.       n²/m

7) How many terms of the series 1+3+ 9+27+... must be taken so that the sum is 9841 ?     9

8) If a be the first term, l the nth term and p the product of the first n terms of a GP, show that, p²= (al)ⁿ.

9) Find three numbers in GP whose sum is 13/12 and product is -1.       3/4,-1,4/3 or 4/3,-1,3/4

10) If a, b, c are in GP, show that
a) a²+ b², ab+ bc and b²+ c² are also in GP
b) a²b²c²(1/a³+ 1/b³ + 1/c³)= a³+b³+ c³.

11) Insert six geometric means between 56 and 7/16.      28,14,7,7/2,7/4,7/8

12) Sri S. Roy borrows Rs32760 without interest and agrees to pay back in 12 monthly installments , each installment being twice the proceeding one. Find the amounts of second and last installments.         16384

13) If a,b,c are in GP and a¹⁾ˣ = b¹⁾ʸ = c¹⁾ᵏ, show that x, y, z are in AP .

14) The sum of three numbers in AP is 18; if 2, 4 and 11 be added to them respectively, the resulting numbers are in GP. Determine the numbers .     3,6,9

15) Find the sum to n terms:
a)  4+ 44 + 444+....            40/81 (10ⁿ-1)-4n/9
b) 0.7 +0.77+ 0.777+.....            7/9{n - 1/9(1- 1/10ⁿ)}

16) if 5, x, y, z, 405, are the first 5 terms of a GP, find the value of x,y,z.    15,45,135

17) The second term of a GP is b and the common ratio is r. If the product of the first three terms of this GP is 64, find b.           4

18) Find the 10th and the pth terms of the GP 2, 6,18, 54...     2.3⁹ , ᵖ⁻¹

19) Find the 9th and 1th terms of the GP  4, -8,16, -32.....      1024

20) Find the 14th and the nth terms of the GP √5,1, 1/√5, 1/5,..... 1/5⁶ 5¹⁻ ⁿ⁾²

21) If the third term of GP is the square of the first term and its fifth term is 729, find the GP .            9,27,81... or 9,-27,81,-243

22) if the (p + q)th term of a GP is a and (p - q)th term is b, determine its Pth term.    ±√(ab)

23) If the nth term of a GP be p, then show that the product of its first (2n -1) terms is p²ⁿ⁻¹.

24) Which term of the GP √2, √6, 3√2, 3√6,....is 243√2 ?       11

25) Is 256 a term of the GP 3, 6, 12, 24....      no

26) Find r if
a) 3r+1, 7r, 10r+8 are in GP.        2, -4/19
b) 2r, 4r+1, 6r+2 are in GP.            -1/2

27) Insert three geometric means between 7/4 and 56.       7/2,7,14,28

28) If three unequal positive numbers a,b,c are in GP then show that a+ c >2b

29) Three different numbers a,b,c are both in AP and GP -- is it possible?   No

30) The AM of two numbers is 10 and their GM is 8. Find the numbers.   16,4

31) if the 4th term of a series in geometric progression is 24 and 7th term is 192, find the sum of its first 10 terms.      3069

32) How many terms of the series 64+ 32+16+8 +...must be taken so that sum may be 255/2?    8

33) A GP has first term 3 and the last term 48. if each term is twice the preceding , find the number of terms and the sum of the GP.       5 , 93

34) The sum of the first 8 terms of a GP is five times the sum of the first four terms. Find the common ratio.     ±√2 or 1

35) The sum of the first 4 terms of a GP is 40 and the sum of first 8 terms is 3280. Obtain the GP.     1,3,9,27 or -2,6,-18,54...

36) Find the three number in GP whose sum is 14 and product is 64.    2,4,8 or 8,4,2

37) Three rational numbers x,y,z are in GP. Sum of the number is 65 and the product of the first and third numbers is 225. Find the common ratio of the GP.    3 or 1/3

38) Find the three terms in GP whose products is 729 and the sum of their product in pairs is 351.       3,9,27 or 27,9,3

39) If a, b, c and d are in GP, show that
a) (a -b)², (b - c)², (c - d)² are in GP
b) a²+ b², b²+ c², c²+ d² are in GP
c) a²+ b²+ c², ab+ bc+ CD, b²+ c²+ d² are in GP
d) (b - c)²+ (c - a)²+(d - b)²= (a - d)²

40) If three numbers a,b,c satisfy the relation (a²+ b²)( b²+ c²)= (ab+b c)², show that a,b,c are in GP.         

41) A boy saves 1 paise the first day, 2 paise the second day, 4 paise the third day and 8 paise the fourth day and so on. Find his total savings at the end of 10 days.     Rs10.23

42) 6000 to decrease amount with interest 1.38 in 10 monthly installment each installment been try the presiding once find the second in the last installment 19682 without interest to repair the money in the monthly installment price the presiding once after the seven the common nation of the series in GPS 3 the sum of the first in the third term is equals to the sum of the squares of the first in the second terms find the sum of n terms is equal to 6 so that the sum is 64 the sum of three numbers in GPS 70 rupees to exchange the multiplied by 4 and the mean by 5 the product inserted between two given number then prove that the sum of the three numbers in AP is 15 14 and 19 to the number the resulting numbers are in GP final numbers the sum of the three numbers in AP 2 2 6 or I will respectively to first second third numbers the resulting numbers three terms are in repeat the product is 2164 be added to the first time and 6 on the second term the resultant number and terms in GP find the sum and terms of each of the following one 111 to 222

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