Question

How many terms of the AP: -6, -11/2, -5, -9/2, ,……, are needed to give their sum as zero.

Answer 1

Answer:

n=23

Step-by-step explanation:

Sum of n numbers of an AP is given by

$\frac{n}{2} (2a + (n - 1)d)$

Here

a=-6

d=0.5

Using the condition given in the question

$\frac{n}{2} (2 \times - 6 + (n - 1) \times \frac{1}{2} ) = 0$

$- 12 = \frac{1}{2} (1 - n)$

n=23

Answer 2

Concept

Recall the formula of sum of AP is S = n/2[2a + (n − 1) × d]

where

$a_n$ = the nᵗʰ term in the sequence

$a_1$ = the first term in the sequence

d = the common difference between terms

Given

The AP: -6, -11/2, -5, -9/2,……

To find

We need to find how many terms of a series are zero.

Solution

The common difference between terms d is -11/2-(-6) =1/2.

The first term of the series is -6.

then the sum when zero

0 = n/2[2(-6) + (n − 1) × 1/2]

0 = -12 + 1/2(n − 1)

12 =  1/2(n − 1)

n = 23

Hence starting 23th term sum is zero.