Question

Find the value of the middle most term (s) of the AP : -11, -7, -3,..., 49.

Answer 1

a = -11

d = 3

49 = -11+(n-1)3

63 = 3n

n = 21

middlemost term = 11th term = -11+10(3) = 19

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Answer 2

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Find the value of the middle most term (s) of the AP : -11, -7, -3,..., 49.

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.Given :

• AP : -11, -7, -3,...,49

To Find :

• Middle most term (s)

Solution :

$\huge\sf\rightarrowtail$ Here, first term = a = -11 and

Common difference = d = -7 - (-11)

$\sf\huge\implies$ -7 + 11

$\sf\huge\implies$ 4

If the given AP consists of n terms , Then

$\rightarrow[tex]\a_{n}$ = 49

$\sf\huge\implies$ If the given AP consists of n terms , then a_ n = 49

$\sf\huge\implies$ a + (n - 1) = 49

$\sf\huge\implies$ -11 + (n -1) ×4 = 49

$\rightarrowtail$ 4 (n - 1) = 60

$\rightarrowtail$ n - 1 = 15

$\sf\huge\implies$$\color{red} {n\: =\: 16}$

So, the given AP consists of 16 terms

As 16 is even ,there will be two middle terms which are $\frac{16}{2}$ th term and $\frac{16}{2}$ +8th term and 9th term

$\star$ Now , 8 th term is:

$\huge\sf\rightarrowtail$ a + (8 - 1)

$\huge\sf\rightarrowtail$ d = -11 + 7 × 4

$\huge\sf\rightarrowtail$ -11 + 28

$\sf\huge\implies$$\color{red} {17}$

$\star$ Now, 9th term is :

$\huge\sf\rightarrowtail$ a + (9 - 1)

$\huge\sf\rightarrowtail$ d = -11 + 8 × 4

$\huge\sf\rightarrowtail$ -11 + 32

$\sf\huge\implies$$\color{red} {21}$

Hence , the values of the two middle most term are 17 and 21

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