How many terms of the AP 4, 11, 18, ______ will make the sum 795?
15
For the AP 4, 11, 18, ..., the first term a = 4 and the common difference d = 11 - 4 = 7.
Sum of n terms, Sn = n/2 [2a + (n-1)d]. Setting Sn = 795 gives n/2 [8 + 7(n-1)] = 795.
This simplifies to n(7n + 1) = 1590, that is 7n^2 + n - 1590 = 0.
Solving this quadratic equation, n = (-1 + sqrt(1 + 44520))/14 = (-1 + 211)/14 = 210/14 = 15.
So 15 terms of the AP make the sum 795.
Important Questions from Arithmetic Progression
What is the arithmetic mean of first 8 multiples of 13?
The average of five consecutive odd natural numbers is 27. The product of the first and fifth number is:
Find the sum of all the numbers between 100 to 200 which are divisible by 12.
In a garden, there are 6 daisy plants the first year. Each year, a gardener adds 3 new daisy plants the first year and loses 2 each year. He has 26 jasmine plants the first year and loses 2 each year. When will the number of daisy plants equal the number of jasmine plants after the first year?
The first and last terms of an A.P. are 18 and 48. If the sum of its terms is 396, then the number of terms will be?
