Question

How many terms of the ap 24,21,18,.......Must be taken so that their sum is 78?

Answer 1

24,21,18,..............

Let a and d be the first term and common difference respectively

First Term = a = 24

Common Difference = d = -3

Let sum of the terms be 78

From the formula,

Sum of terms= n/2[2a+(n-1)d]

→78=n/2[2(24)+(n-1)(-3)]

→156=n[48-3n+3]

→156=51n-3n²

→3n²-51n+156=0

→n²-17n+52=0

→n²-13n-4n+52=0

→n(n-13)-4(n-13)=0

→(n-13)(n-4)=0

•When n-13=0,

n=13

Taking 13 terms from first would give 78 as sum of the terms

•When n-4=0,

n=4

Taking 4 terms from last gives 78 as the sum.

Thus, n= 13 or 4

Answer 2

Step-by-step explanation:

Hi,

AP = 24 , 21 , 18

Here,

First term ( a )= 24

Common difference ( d ) = 21 - 24 = -3

Sn = N/2 × [ 2a + ( n - 1 ) * d ]

78 = n/2 × [ 2*24 + ( n -1 ) * -3 ]

156 = 51n - 3n²

3n² - 51n +156 = 0

3 ( n² - 17n + 52 ) = 0

n² - 17n + 52 = 0

n² - 13n - 4n + 52 = 0

n ( n - 13 ) -4 ( n - 13 ) = 0

( n - 13 ) ( n - 4 ) = 0

n = 13 or n = 4.

Hope it will help you:)