Question

how many terms of AP 18,16,14,.... should be taken so their sum is zero?

Answer 1

Hello friend your answer........

Here,
a=18 , d=16-18=-2 , Sn=0





I hope it helps you

Answer 2

AP series = 18, 16, 14 ....

⇒ First Term = a1 = 18

⇒ Common difference = a2 - a1 = 16 - 18 = -2

Express the an term in n:

an = a1 + ( n - 1 )d

an = 18 + (-2)(n - 1)

an = 18 - 2n + 2

an = 20 - 2n

Find n:

Sn = n/2 (a1 + an)

0 = n/2 (18 + 20 - 2n)

0 = n/2 ( 38 - 2n)

38n - 2n² = 0

2n² - 38n = 0

2n (n - 19) = 0

n = 0 or n = 19

Answer: 19 terms will make the sum 0.