Question

How many terms of the AP 65, 60, 55, ........... be taken so that their sum is zero ?

Answer 1

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Answer 2

Answer

27 terms of the given AP are required so that their sum becomes 0

Given

• The AP is 65,60,55,........

To Find

• How many terms of the given AP to be taken so that their sum is 0

Solution

Given , the AP

65 , 60 , 55 , ...…...

Here ,

first term , a = 65

Common difference , d = -5

Let us consider sum upto ‘n’ terms be 0

Now we know that ,

$\sf \longrightarrow S_{n} = \dfrac{n}{2}\{ 2a + (n -1)d \} \\\\ \sf\implies 0 = \dfrac{n}{2} \{2\times 65 + (n - 1)(-5) \} \\\\ \sf\implies 0 = n\{ 130 - 5n + 5 \} \\\\ \sf\implies n\{135 - 5n \} = 0 \\\\ \sf\implies 5n -135= 0 \\\\ \sf\implies 5n = 135 \\\\ \sf\implies n = 27$

Thus 27 terms of the given AP must be taken so that their sum becomes 0