Question
The sum of the first 163 terms of a GP is equal to the
sum of the first 161 terms in the same GP. If the 117th term in the same GP is 985, then what will be the sum of 150 terms?Solution
According to the question, if we take a(r163-1)/ r-1 =a(r161-1)/r-1 r163 = r161 r2 =1 r=±1 r = +1, the sum will be undefined. Taking r = -1, T117 = ar117-1 985 = a (-1)116 a=985 S150 =a(1-r")/1-r (r 985(1-(-1)150)/1+1 985(1-1)/2=0 =0
The ratio of two numbers is 4:9. If each number is decreased by 4, the ratio becomes 3:7. Find the smaller numbers.
- A total of Rs. ‘K’ was to be distributed among P, Q, and R in ratio of 7:5:6 respectively but due to some reason the money was falsely distributed in r...
84 is divided into two parts in such a way that the fourth part of the first part and the fifth part of the second are in the ratio 1 : 2. The first par...
Two numbers are respectively 40% and 20% more than a third number. Find the ratio of two numbers.
What number has to be added to each term of 2:5 to make the ratio 6:7?
Divide Rs. 2541 among Deepa and Deepak in the ratio (11/8) : (11/6) ?
Incomes of company A and company B are in the ratio of 3:7. Had the income of company A been more by Rs.20 lakh, the ratio of their incomes would have b...
P, Q and R together started a business. Four times the investment of P equals five times the investment of Q and the capital of Q is twice that of R. Fi...
- Find the fourth proportion of (2k - 5), (k + 1), and (3k + 4). (Note: 'k' is the smallest two-digit prime number.)
- Initially, a bag contains t-shirts of two colours (yellow and green) in the ratio of 7: 15 respectively. If 19 yellow t-shirts and 11 green t-shirts were d...
Relevant for Exams:
