Question

find the number of terms of the AP 42,39,36....so that their sum is 0?

Answer 1

Answer:

the number of terms of AP so that sum the terms is zero is 27

Step-by-step explanation:

Given series of AP =  42, 39, 36, ...

first term a = 42

common difference d = 42 -39 = -3

we need to find number of terms so that sum of the all terms is zero

sum of terms in AP = $\frac{n}{2} [ 2a + (n-1)d ]$ =0

                          ⇒ $\frac{n}{2} [ 2(42 )+ (n-1) (-3)]=0$

                          ⇒$\frac{n}{2} [84 -3n +3] =0$

                          ⇒$\frac{n}{2} [ 81 -3n] =0$

                          ⇒ $n(81 -3n) =0$

                          ⇒ 3$n^{2}$ =81n

                          ⇒ 3n =81

                          ⇒ n = 27

the number of terms of AP so that sum the terms is zero is 27