Q28 of 167 Page 19

How many terms of the A.P. - 6, - , - 5, …, are needed to give the sum - 25?

given is an AP whose first term is - 6 and d is

To find: the number of terms required to make the sum of a given AP to - 25

we know that the sum of AP is given by the formula:

substituting the values in the above equation

100 = - 25n + n²

n² - 25n + 100 = 0

(n - 20) (n - 5) = 0

solving we get n = 20 or n = 5

If the sum of a certain number of terms of the A.P. 25, 22, 19, …. is 116. Find the last term

Find the sum of odd integers from 1 to 2001.

In an A.P. the first term is 2, and the sum of the first 5 terms is one-fourth of the next 5 terms. Show that 20th term is - 112

If S₁ be the sum of (2n + 1) terms of an A.P. and S₂ sum of its odd terms, then prove that: S₁: S₂ = (2n + 1) : (n + 1).