Question

Sum of 3 terms of an A.P. is 48 then the middle term is A) 8 B) 24 C) 32 D) 16​

Answer 1

Answer:

Given:-

Sum of 3 terms of an A.P. is 48 then the middle term is?

To Find:-

The middle term of an A.P.

Note:-

●》Here; formula of three terms of an A.P. is = a - d, a, a + d. So, sum of three terms of an A.P. = a - d + a + a + d. As from this, middle term is "a". So we will find the value of "a" by adding and transposing the terms.

●》Transposing - For finding unknown value, known value needs to be transposed from its side to another and in this process signs are also changed. For example - Multiple value becomes Divisional value.

Solution:-

$\huge\red{3 \ \ terms \ \ of \ \ an \ \ A.P. = 48}$

$\huge\red{ \ \ Middle \ \ term = ?}$

☆ According to note first point~

▪︎$a - d + a + a + d = 48$

☆ Taking common terms at one side~

▪︎$a + a + a + d - d = 48$

▪︎$2a + a + 0 = 48$

▪︎$3a = 48$

☆ According to note second point ( Transposing )~

▪︎$3 × a = 48$

▪︎$a = \dfrac{48}{3}$

☆ After dividing~

▪︎$a = 16$

$\huge\pink{Middle \ \ term = a => 16}$

Answer:-

Hence, the middle term of an A.P. = 16 ( Option D ).

:)

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.

S=n/2(2a+n-1)d

Given:-

Sum of 3 terms of an A.P. is 48 then the middle term is?

Find:-

The middle term of an A.P.

Solution:-

Let there be three no. a-d,a,a+d

Sum of three terms of an P=48

According to question,

a-d+a+a+d=48

3a=48

a=16

Hence, the middle term of an A.P. = 16 ( Option D ).

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