Solution: Here a = 1000 (staring of first year) and common ration = 1.1 X + y = 50 - ( i) & xy = 49 - (ii)įrom the above equations the number can be 1 & 49Įxample – 1: If an amount ₹ 1000 deposited in the bank with annual interest rate 10% interest compounded annually, then find total amount at the end of first, second, third, forth and first years. Solution: Here x’ and ‘y’ are two numbers then In the given sum a = 1/8, n = 4 and b = 128Įxample-12: ‘x’ and ‘y’ are two numbers whose AM is 25 and GM is 7. G n are said to be Geometric means in between ‘a’ and ‘b’. Solution: Formula – The ‘n’ numbers G 1, G 2, G 3. Here given a 7 = 8 x a 4 and also a 5 = 48Įxample -11: Four geometric means are inserted between 1/8 and 128. Solution:Let first term is ‘a’ and common ratio is ‘r’ for the given geometric sequence What will be the first term when its 5 th is 48? Here a 6 = 24 - ( i) & a 13 = 3/16 -– ( ii)Įxample – 9: The 7 th term of a G.P is eight times of fourth term.
Solution: Let first term is ‘a’ and common ratio is ‘r’ (a +b + c) 2 = a 2 + b 2 + c 2 + 2 (ab + bc + ca) -– ( ii )įrom the above two equations ( i ) & ( ii )Įxample – 8: In a G.P 6 th term is 24 and 13 th term is 3/16 then find 20 th term of the sequence. Now take (a +b + c) 2 as per algebraic formula ⇒ a 2 + b 2 + c 2 = ab + bc + ca -– ( i ) Solution: As per properties of Geometric Progression Įxample – 7 : If (a-b), (b-c), (c-a) are the consecutive terms of G.P then find (a +b + c) 2 I.e Common ratio = r = a 2 / a 1 = a 3 / a 2 = a 4 / a 3 =. SoĮxample – 6: Find ‘a’ so that a, a+2, a+6 are consecutive terms of a geometric progression.
Solution: Here a = 1 and a 4 = 27 and let common ratio is ‘r’. Solution: Let first term of G.P is ‘a’ and common ratio r = 2Ī 15 = 192 x 2 7 = 3 x 2 6 x 2 7 = 3 x 2 13Įxample – 5: In a G.P first term is ‘1’ and 4 th term is ‘ 27’ then find the common ration of the same. So we can find easily by direct multiplication upto required number.Įxample – 4: Find the 15 th term of a G.P Whose 8 th term is 192 and the common ratio is ‘2’ įormula for n th term G.P is a n = ar n-1Įxample- 2: Find the 10 th and n th term of the Geometric sequence 7/2, 7/4, 7/8, 7/16.
Solution : General form of G.P = a, ar, ar 2, ar 3. Geometric progression exercises with answersĮxample – 1 : Write G.P if a = 128 and common ratio r = -1/2 Geometric Sequences Practice Problems | Geometric Progression Tutorialįormulas and properties of Geometric progression In this page learn about Geometric Progression Tutorial – n th term of GP, sum of GP and geometric progression problems with solution for all competitive exams as well as academic classes.
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