Question

Find the middle term of an a.p 9,15,21,27,........,183

Answer 1

Step-by-step explanation:

183=9+(n-1)d=9+(n-1)6=6n+3.

hence n is 30.

this AP has even number of terms so there is no middle term.

Answer 2

The middle term of an A.P are 93 or 99.

Step-by-step explanation:

Given : An A.P. 9,15,21,27,........,183.

To find : The middle term of an A.P ?

Solution : ​

Using the last term formula,

$l=a+(n-1)d$

Where, a=9 is the first term

d=6 is the common difference

l=183 is the last term

Substitute the value,

$183=9+(n-1)6$

$(n-1)6=174$

$n-1=29$

$n=30$

The number of terms is 30 (even).

The middle terms are (n/2)th term and [(n/2) + 1]th term

i.e. 15th term and 16th term

15th term is $a_{15}= a + 14d$

$a_{15}= 9 + 14(6)$

$a_{15}=93$

16th term  is $a_{16}= a + 15d$

$a_{16}= 9 + 15(6)$

$a_{16}=99$

The middle term of an A.P are 93 or 99.

#Learn more

If nth terms of sequence is given by tn=4n-3, then find first three terms of the sequence

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