Question

The sum of n terms of AP 24,21,18.........is 108. Find n

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Concept:

The difference between any two consecutive integers in an arithmetic progression (AP) sequence of numbers is always the same amount. It also goes by the name Arithmetic Sequence. For instance, the natural number sequence 1, 2, 3, 4, 5, 6,... is an example of an arithmetic progression. It has a common difference of 1 between two succeeding terms (let's say 1 and 2). (2 -1). We can see that the common difference between two subsequent words will be equal to 2 in both the case of odd and even numbers.

Sₙ=n/2[2a+(n-1)d]

Tₙ=[a+(n-1)d]

Given:

The sum of n terms of AP 24,21,18.........is 108.

Find:

Find n

Solution:

d=3

Sₙ=n/2[2a+(n-1)d]

108= n/2[2 x 24 -(n-1)3]

216= n[48 -3n+3]

216=-3n²+51n

3n²-51n+216=0

n²-17n+72=0

(n-8)(n-9)=0

n=8,9

Sₙ=8/2[2 x 24 -21]

    =4x27

    =108

Sₙ=9/2[2 x 24-8 x 3]

   =9/2 x 24

   =108

Therefore, the value of n can be 8 and 9

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