Question
Sum of first 10 terms of a GP is equal to the sum of the
first 12 terms in the same GP. Sum of the first 15 terms is 31, what is the third term in the GP?Solution
Sum of first 10 terms is equal to sum of first 12 terms. Sum of first 12 terms = Sum of first 10 terms + 11th term + 12th term 11th term + 12th term = 0 Let 11th term = k, common ratio = r 12th term will be = kr k + kr = 0 k (1 + r) = 0 r = -1 as k cannot be zero Common ratio = -1 Now, sum of 15 terms = a(r - 1)/(r - 1) = 31 ⇒ a(-1 -1)/(-1 -1) = 31 ⇒ a = 31 ∴ Third term = ar = 31 × (-1) = 31
Fresh watermelon contains 60% water. Dry watermelon contains 30% water. From 1 Quintals fresh Watermelon, approximately how many kgs of Dry Watermelon c...
In a mixture of juice & water, 75 litres water is mixed due to which ratio changes from 3:4 to 1:2. Find initial quantity of mixture. (in lit...
- 180 litres of a mixture is made up of juice and soda in the ratio of 4:5, respectively. If 36 litres of the mixture is withdrawn and replaced with the same...
A vessel contains 280 litres of milk and water in the ratio of 9:5. If 20 litres of milk is added to the mixture, then find the ratio of milk to water i...
In an 800 ml mixture, 60% is soda, and the remainder is water. If 96 ml of soda and 128 ml of water are added to this mixture, determine the new ratio o...
A 120 litres solution of alcohol and water contains 30% alcohol. When Q litres of alcohol and (Q - 4) litres of water are added to the solution, the qua...
- A mixture contains wine and water in the ratio 5:6. After removing 132 ml of mixture and adding 264 ml of water, the amount of water becomes 100% more than...
A vessel contains 120 liters of a mixture in which oil and water are in the ratio 2:3. If 40 liters of this mixture are taken out and 'x' liters of oil ...
A container holds 80 litres of a solution which has milk and water in the ratio 3:2. 40 litres of this solution is taken out, and then 10 litres of wate...
A mixture of milk and water contains 40% water. On adding 15 litres of water, the quantity of milk becomes 20% more than that of water. Find the initial...
Relevant for Exams:
