Question

Find the middle term of the ap: 6,13,20.....,223

Answer 1

$\bold\red{\underline{\underline{Answer:}}}$

$\bold{111 \ and \ 118 \ are \ middle \ terms.}$

$\bold\orange{Given:}$

The given A.P. is 6,13,20,...,223

$\bold\pink{To \ find:}$

Middle terms.

$\bold\green{\underline{\underline{Solution}}}$

The given A.P. is 6,13,20,...,223

Here,t1=a=6,d=13-6=7 and tn=223

tn=a+(n-1)d.... formula

223=6+(n-1)7

(n-1)7=223-6

(n-1)7=217

n-1=$\bold{\frac{217}{7}}$

n-1=31

n=31+1

n=32

Middle terms are 16th and 17th terms

t16=6+(16-1)7

t16=6+105

t16=111

t17=t16+d

t17=111+7=118

Therefore,

$\bold\purple{111 \ and \ 118 \ are \ middle \ terms.}$

Answer 2

Answer:

Step-by-step explanation:

The given A.P. is 6,13,20,...,223

Here,t1=a=6,d=13-6=7 and tn=223

tn=a+(n-1)d.... formula

223=6+(n-1)7

(n-1)7=223-6

(n-1)7=217

n-1=

n-1=31

n=31+1

n=32

n/2 is the middle term

Middle term is 16 th

t(16)=6+(16-1)7

t(16)=6+105

t(16) = 111

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