Math, asked by aniruddhasaini, 10 months ago

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

Answers

Answered by Anonymous
4

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

Answered by Anonymous
8

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

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