Loan 5

Abdul takes a loan of 200000 from Ali and agrees to repay in number of instalment, each instalment begin with the 2nd exceeding the previous one by 1000, if the first instalment is 500, find how many instalment will be necessary to be wipe out
the loan? Completely

Correct answer:

n =  20

Step-by-step explanation:

$$\begin{gathered} a=200000 \\ {a}_1=500 \\ d=1000 \\ a={\displaystyle \frac{a_1+a_n}{2}}n \\ a={\displaystyle \frac{a_1+a_1+(n-1)\cdot d}{2}}\cdot n \\ 200000\ast 2=(500\ast 2+(n-1)\ast 1000)\ast n \\ 200000\cdot 2=(500\cdot 2+(n-1)\cdot 1000)\cdot n \\ -1000n^2+400000=0 \\ 1000n^2-400000=0 \\ a=1000;b=0;c=-400000 \\ D=b^2-4ac=0^2-4\cdot 1000\cdot (-400000)=1600000000 \\ D>0 \\ {n}_{1,2}={\displaystyle \frac{-b\pm \sqrt{D}}{2a}}={\displaystyle \frac{\pm \sqrt{1600000000}}{2000}} \\ {n}_{1,2}={\displaystyle \frac{\pm 40000}{2000}} \\ {n}_{1,2}=\pm 20 \\ {n}_1=20 \\ {n}_2=-20 \\ \text{ Factored form of the equation: } \\ 1000(n-20)(n+20)=0 \\ n=n_1=20 \end{gathered}$$

Our quadratic equation calculator calculates it.

Try another example

Related math problems and questions:

• Geometric progression
  In geometric progression, a1 = 7, q = 5. Find the condition for n to sum first n members is: sn≤217.
• Find the sum
  Find the sum of all natural numbers from 1 and 100, which are divisible by 2 or 5
• Loans, loan ...
  In Slovakia, launched a short-term non-bank loans, of which few people have their "take" are considered unfavorable. Often, the borrower ends up in a spiral of debt, which takes more and more onerous loan used to repay earlier loans. Calculate how many 9-
• The sum
  The sum of the first 10 members of the arithmetic sequence is 120. What will be the sum if the difference is reduced by 2?
• Insert into GP
  Between numbers 5 and 640, insert as many numbers to form geometric progression so the sum of the numbers you entered will be 630. How many numbers must you insert?
• Five-digit numbers
  How many different five-digit numbers can be created from the numbers 2,3,5 if the number 2 appears in the number twice and the number 5 also twice?
• Microorganisms
  The first generation of micro-organisms has a population of 13500 members. Each next generation is 11/10 times the previous one. Find out how many generations will reach at least three times members of the first generation.
• Two geometric progressions
  Insert several numbers between numbers 6 and 384 so that they form with the given GP numbers and that the following applies: a) the sum of all numbers is 510 And for another GP to apply: b) the sum of entered numbers is -132 (These are two different geome
• Curiosity factor
  A blogger starts a new website, initially the number of the traffic is 293 due to their curiosity factor. The business owner estimated that the traffic will increase by 2,6% per week. What will be the number of it in week 5?.
• Sum 1-6
  Find the sum of the geometric progression 3, 15, 75,… to six terms.
• Bonuses
  Five employees of the company were paid bonuses so that each successor received 550 USD less than the previous employee. How much did everyone get if a total of USD 11,000 has paid?
• Geometric progression 2
  There is geometric sequence with a₁=5.7 and quotient q=-2.5. Calculate a₁₇.
• The Hotel
  The Holiday Hotel has the same number of rooms on each floor. Rooms are numbered with natural numerals sequentially from the first floor, no number is omitted, and each room has a different number. Three tourists arrived at the hotel. The first one was in
• Present value
  A bank loans a family $90,000 at 4.5% annual interest rate to purchase a house. The family agrees to pay the loan off by making monthly payments over a 15 year period. How much should the monthly payment be in order to pay off the debt in 15 years?
• Five element
  The geometric sequence is given by quotient q = 1/2 and the sum of the first six members S₆ = 63. Find the fifth element a₅.
• A five-digit
  A five-digit odd number has the sum of all digits (digits) five and contains two zeros. If we move each digit in the number one place to the left and move the first digit to the last place, we get a number 20,988 smaller. Find this unknown five-digit numb
• Find x 2
  Find x, y, and z such that x³+y³+z³=k, for each k from 1 to 100. Write down the number of solutions.