Question

find the sum of two middle terms of the A. P -4/3,-1,-2/3,-1/3,..........,4 1/3​

Answer 1

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$- \frac{4}{3} | - 1 \: | - \frac{2}{3} | - \frac{1}{3} | .............. | 4 \frac{1}{3}$

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Firstly we have to find n of A.P,

$A_{n}=a+(n-1)d$

$\frac{13}{3}=-\frac{4}{3}+(n-1)\frac{1}{3}$

$\frac{17}{3}\times 3=n-1$

$n=18$

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We have to find middle terms

So,

$a_{9}=a+8d$

$a_{9}=-\frac{4}{3}+8\frac{1}{3}$

$a_{9}=\frac{8}{3}-\frac{4}{3}$

$a_{9}=\frac{4}{3}$

There are two terms so we can take 8 as second value of n

$a_{8}=-\frac{4}{3}+\frac{7}{3}$

$a_{8}=\frac{7-4}{3}$

$a_{8}=1$

Add both

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$1+\frac{4}{3}$

$\frac{7}{3}$

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