Progressions Read Discuss Courses Progressions Please wait while the activity loads. If this activity does not load, try refreshing your browser. Also, this page requires javascript. Please visit using a browser with javascript enabled. If loading fails, click here to try again Question 1 Calculate the arithmetic mean of the given series: 2, 6, 10, 14, 18, 22, 26, 30. 8 16 32 None of the above Progressions Discuss itQuestion 1-Explanation: AM = (a1+a2+a3+......+an)/n=(n(a1+an)/2)/n=(a1+an)/2 = (2 + 30)/2 = 16 Question 2Find the Sum of series: 2, 6, 10, 14, 18, 22, 26, 303288128110Progressions Discuss itQuestion 2-Explanation: Sum of AP = (n/2)[2a+(n-1)d] = 4*[4+7*4] =128 Question 3 Find the Arithmatic mean of series: 10, 7, 4, 1, -2 13/2 14/3 4 16/5 Progressions Discuss itQuestion 3-Explanation: Arithmatic Mean = (a1+a2+a3+......+an)/n =(n(a1+an)/2)/n =a1+a2/2 =10-2/2 = 4 Question 4Find the Sum of series: 10, 7, 4, 1, -2 40212018Progressions Discuss itQuestion 4-Explanation: Sum of series = (n/2)[2a+(n-1)d] = 20 Question 5 Find sum of series: 2, 2.5, 3, 3. 5, 4, 4. 5..........11 120 123.5 126.5 118.5 Progressions Discuss itQuestion 5-Explanation: To, find the number of terms in the Ap Tn = a+(n-1)*d11 = 2+(n-1)*0.5So, we get n = 19 sum of AP = (n/2)[2a+(n-1)d]n=19, a=2, d=1/2S = (19/2)[2*2+(19-1)1/2]=(19/2)[4+9] =9.5*13 = 123.5 Question 6Find Arithmetic Mean of series: 2, 2.5, 3, 3. 5, 4, 4. 5..........1113/225/81922/9Progressions Discuss itQuestion 6-Explanation: Arithmetic mean AM of the series is given by = (a1+a2+a3+.....+an)/n ……… (1) But the given series is also an AP which sum is given by = (n/2)*(a1+an) ………..(2) From equation (1),(2) we get, AM=(a1+an)/2 AM=(2+11)/2=13/2 Question 7 Find the sum of series: 1, 3, 9, 27, 81, ..............39 [(1-3^(10))]/(1-3) 18 10 20 Progressions Discuss itQuestion 7-Explanation: Sol: Sn=[a(1-rn)]/(1-r) =[1(1-310)]/(1-3) =[(1-310)]/(1-3) Question 8 Calculate the sum of given series: 1/3, 1/9, 1/27, 1/81................. 1/4 1/3 1/2 1 Progressions Discuss itQuestion 8-Explanation: The given series is an infinite GP, whose sum is given by Sn=a/(r-1) Where, a=first term of series, r=common ratio. Therefore, Sn=(1/3)/(1-1/3) Sn=1/2 Question 9 For n positive integers, if their product is nn, then what will be their sum? Equal to n+(1/n) Equal to n A negative integer Never less than n2 Progressions Discuss itQuestion 9-Explanation: Clearly, since the given integers are positive, their sum can't be negative. Also, since the numbers are all integers their sum can't be a fraction. Let's take 1, 3 and 9. The product of these three integers is 27 = 33. This can also be written as nn where n=3. As we can see, the sum of these 3 integers is not equal to 3. Therefore, we are left with the fourth option. Question 10 A tennis ball is initially dropped from a building of height 180 m. After striking the ground, it rebounds (3/5)th of the height from which it has fallen. Calculate the total distance that the ball traveled before it comes to rest. 540 m 600 m 900 m None of the above Progressions Discuss itQuestion 10-Explanation: The total distance traveled by the ball is the sum of two infinite series: a. Series 1: the distance traveled by the ball when it's falling down b. Series 2: the distance traveled by the ball when it's bouncing up S1 = a1 / (1 - r1) and S2 = a2 / (1 - r2) S1 = 180 / (1 - 3/5) and S2 = (180 * 3/5) / (1 - 3/5) S1 = 180 / (2/5) and S2 = 108 / (2/5) S1 = 180 * 5/2 and S2 = 108 * 5/2 S1 = 450 and S2 = 270 Therefore, S = S1+S2 = 720 m. 12 There are 15 questions to complete. You have completed questions question Your accuracy is Correct Wrong Partial-Credit You have not finished your quiz. If you leave this page, your progress will be lost. Correct Answer You Selected Not Attempted Final Score on Quiz Attempted Questions Correct Attempted Questions Wrong Questions Not Attempted Total Questions on Quiz Question Details Results Date Score Hint Time allowed minutes seconds Time used Answer Choice(s) Selected Question Text Need more practice! Keep trying! Not bad! Good work! Perfect! Last Updated : 27 Sep, 2023