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
If the nth term of a sequence is \(\frac{2 n+5}{7}\), then what is the sum of its first 140 terms?
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?
