Find the value of the middle most term(s) of the A.P. -11, -7, -3, ……., 49.

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Hint: First we need to find out the position of the last term of the given A.P. i.e. 49 using the formula  $ {{a}_{n}}=a+(n-1)d $  where a is first term, d is the common difference of the A.P. and  $ {{a}_{n}}=49 $. Suppose 49 is at  $ {{n}^{th}} $  position in the A.P. then, if n is even then middle terms of the A.P. will be  $ \dfrac{n}{2},\dfrac{n}{2}+1 $ and if n comes out to be an odd number then middle term will be  $ \dfrac{n+1}{2} $. After that we will find the value of the middle term using the same formula.Complete step-by-step answer:First we need to find out the position of the last term of the given A.P. i.e. 49 using the formula  $ {{a}_{n}}=a+(n-1)d $ , wherea is first term,d is the common difference of the A.P. i.e. = - 7- (-11) = 4, $ {{a}_{n}}=49 $ .So by applying the formula and putting the required values in it, we get49 = - 11 + (n-1)  $ \times  $  4After further simplifying, we get $ n-1=\dfrac{49+11}{4} $  $ \begin{align}  & n-1=\dfrac{60}{4} \  & n-1=15 \  & n=16 \ \end{align} $ Hence 49 is at the  $ {{16}^{th}} $  place in the given A.P.And we know that 16 is an even number so we will get two terms in the middle of the A.P. and their position will be  $ \dfrac{n}{2},\dfrac{n}{2}+1 $  where n = 16,So now we get,  $ \dfrac{16}{2},\dfrac{16}{2}+1 $  as our middle most terms i.e.  $ {{8}^{th}}\,and\,{{9}^{th}} $  term of the A.P.We will find the values of  $ {{8}^{th}}\,and\,{{9}^{th}} $  terms of the A.P. $ {{8}^{th}} $  term of the A.P. is given by,$$\begin{align}  & {{a}_{8}}=-11+(8-1)\times 4 \  & {{a}_{8}}=-11+7\times 4 \  & {{a}_{8}}=-11+28 \  & {{a}_{8}}=17 \ \end{align}$$Now we will find the  $ {{9}^{th}} $  term of the A.P. $ \begin{align}  & {{a}_{9}}=-11+(9-1)\times 4 \  & {{a}_{9}}=-11+8\times 4 \  & {{a}_{9}}=-11+32 \  & {{a}_{9}}=21 \ \end{align} $ Hence, value(s) of the middle most terms of the given A.P. are 17 and 21Note: You need to remember whenever there are even numbers of terms then there will be two middle terms and when there are a middle number of terms there is only one middle term. And also remember the formula that  $ {{n}^{th}} $  term of the A.P. is given by  $ {{a}_{n}}=a+(n-1)d $  where a is first term and d is common difference of the A.P.

Find the value of the middle most term(s) of the A.P. -11, -7, -3, ……., 49.

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Find the value of the middle most term(s) of the A.P. -11, -7, -3, ……., 49.

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