Question

❤️❤️❤️HELLO FRIENDS ❤️❤️❤️❤️

please solve this question

Answer 1

$\underline{\underline{\large{\mathfrak{Solution : }}}}$



$\underline{\mathsf{Given \: A.P. \longrightarrow \dfrac{-4}{3} , -1 , \dfrac{-2}{3}, \dfrac{-1}{3},....., 4\dfrac{1}{3}.}}$



$\textsf{Here,} \\ \\ \mathsf{\implies First \: term(a) \: = \: \dfrac{-4}{3}} \\ \\ \mathsf{\implies Common \: difference (d) \: =\: -1 \: - \: \Bigg(\dfrac{-4}{3} \Bigg)} \\ \\ \qquad \qquad \qquad \qquad \qquad \: \: \: \: \: \: \: \: \: \: \: \mathsf{ = \: \dfrac{-3 \: + \: 4}{3} \: = \: \dfrac{1}{3}} \\ \\ \mathsf{\implies Last \: term(l) \: = \: 4\dfrac{1}{3} \: = \: \dfrac{13}{3} }$



$\mathsf{Using \: Formula :} \\ \\ \boxed{\mathsf{\implies l \: = \: a \: + \: ( n \: - \: 1)d}}$


$\mathsf{ \implies \dfrac{13}{3} \: = \: \dfrac{ - 4}{3} \: + \: (n \: - \: 1) \dfrac{1}{3} } \\ \\ \mathsf{ \implies \dfrac{13}{ \cancel{3}} \: = \: \frac{ - 4 \: + \: n \: - \: 1}{ \cancel{3}} } \\ \\ \mathsf{ \implies 13 \: = \: n \: - \: 5} \\ \\ \mathsf{ \implies n \: = \: 13 \: + \: 5} \\ \\ \mathsf{ \therefore \quad \: n \: = \: 18}$



$\textsf{Now, 2 middle most terms are 9th and 10th terms.}$



$\underline{ \textsf{So,}} \\ \\ \mathsf{= T_{9} \: + \: T_{10}} \\ \\ \mathsf{= a \: + \: ( 9 \: - \: 1)d \: + \: a \: + \: ( 10 \: - \: 1)d} \\ \\ \mathsf{= 2a \: + \: 8d \: + \: 9d } \\ \\ \mathsf{= 2a \: + \: 17d } \\ \\ \mathsf{= 2\Bigg(\dfrac{-4}{3}\Bigg) \: + \: 17\Bigg(\dfrac{1}{3} \Bigg)} \\ \\ \mathsf{= \dfrac{-8}{3} \: + \: \dfrac{17}{3}} \\ \\ \mathsf{= \dfrac{-8 \: + \: 17}{3}} \\ \\ \mathsf{= \dfrac{9}{3}} \\ \\ \mathsf{ = 3}$



$\boxed{\large{\mathsf{The \: required \: answer \: is \: 3.}}}$

Answer 2

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







Refer to the attachment above for your solution









$\textbf{Hope it helps!}$