Question

find the middle terms of the AP: 6, 13, 20,...,223.

Answer 1

Given :

• First term ( a ) = 6

• Common difference ( d ) = 7

• Last term ( An ) = 223

To Find :

• Middle term of given A.P

Solution :

First we have to find Total no. of term by A.P formula

$\large \boxed{ \sf A_n = a + (n - 1)d} \\ \\ \sf \implies223 = 6 + (n - 1)7 \\ \\ \sf \implies223 - 6 = (n - 1)7 \\ \\ \sf \implies217 = (n - 1)7 \\ \\ \sf \implies \frac{217}{7} = n - 1 \\ \\ \sf \implies31 = n - 1 \\ \\ \large \implies \boxed{\boxed{ \sf n = 32}}$

There are total 32 terms in given A.P. and 16th term is the middle term

$\implies \sf A_{16} = a + 15d \\ \\ \implies \sf A_{16} = 6 + 15 \times 7 \\ \\ \implies\sf A_{16} = 6 + 105 \\ \\ \implies \large \boxed{\boxed{ \sf A_{16} = 111 }}$

111 is the middle term of the A.P

Answer 2

Answer:

Given :

First term ( a ) = 6

Common difference ( d ) = 7

Last term ( An ) = 223

To Find :

Middle term of given A.P

Solution :

First we have to find Total no. of term by A.P formula

An = a + ( n-1) d

=>223 = 6 + ( n-1 ) 7

=>31 = (n-1)

=>n = 32

There are total 32 terms in given A.P. and 16th term is the middle term

=>A16 = a+ 15d

=>A16 = 6+105

=>A16 = 111

111 is the middle term of the A.P