Question

. If the sum of three numbers in A.P is 18, then what is the middle term?
(i) 6
(ii) 4
(iii) 8
(iv) 10​

Answer 1

Answer:

6

Step-by-step explanation:

4 , 6 , 8 can be the arithmetic progression

Answer 2

Concept:

Arithmetic progression is the sequence of numbers in which the difference between the previous and next term or the consecutive terms is constant.

Given:

We have,

The sum of three numbers in A.P is 18.

Find:

We are asked to find the middle term.

Solution:

We have,

The sum of three numbers in A.P is 18.

i.e.

Sₙ = 18

And,

n = 3

So,

According to the given definition,

The middle term = a + d

Now,

Using the formula of sum Arithmetic progression,

i.e.

Sₙ = n/2[2a + (n - 1)d]

Now,

Putting values,

We get,

18 = (3/2) [2a + (3 - 1)d]

On solving,

We get,

12 = 2a + 2d

i.e.

12 = 2(a + d)

i.e.

a + d = 6

i.e.

The middle term = 6

Hence, the middle term of the given A.P. is 6.

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