Question

Please solve the above question with explanation​

Answer 1

$\huge\boxed{Question}$

To find the middle term of the A.P. 19, 16, 13, 10,....., - 53.

$\huge\boxed{Answer}$

$19, 16, 13, 10,......, - 53$

$a \: (first \: term) = 19$

$d \: (common \: difference) = {t}(2) - {t}(1)$

$d = 16 - 19 = - 3$

$\underline\boxed{d = - 3}$

$l \: (last \: term) = - 53$

$n(no.of \: terms) = \frac{l - a}{d} + 1$

$n = \frac{ - 53 - 19}{ - 3} + 1$

$= \frac{ - 72}{ - 3} + 1$

$= 24 + 1$

$\underline\boxed{n = 25}$

${n}^{th} term = {t}(n) = a + (n - 1)d$

$Therefore, \: the \: middle \: terms are \\ {t}(12) or {t}(13)$

${t}(12) = a + 11d = 19 + 11( - 3) = - 14 \\ {t}(13) = a + 12d = 19 + 12( - 3) = - 17$

Therefore the middle terms are - 14 and - 17.

Answer 2

Answer:

$19,16,13,10,......,−53</p><p></p><p>a \: (first \: term) = 19a(firstterm)=19</p><p></p><p>d \: (common \: difference) = {t}(2) - {t}(1)d(commondifference)=t(2)−t(1)</p><p></p><p>d = 16 - 19 = - 3d=16−19=−3</p><p></p><p> \underline\boxed{d = - 3} </p><p></p><p> l \: (last \: term) = - 53 </p><p></p><p> n(no.of \: terms) = \frac{l - a}{d} + 1 </p><p></p><p> n = \frac{ - 53 - 19}{ - 3} + 1 </p><p></p><p> = \frac{ - 72}{ - 3} + 1 </p><p></p><p> = 24 + 1 </p><p></p><p> \underline\boxed{n = 25} </p><p></p><p> {n}^{th} term = {t}(n) = a + (n - 1)d </p><p></p><p> \begin{lgathered}Therefore, \: the \: middle \: terms are \\ {t}(12) or {t}(13)\end{lgathered} </p><p></p><p> \begin{lgathered}{t}(12) = a + 11d = 19 + 11( - 3) = - 14 \\ {t}(13) = a + 12d = 19 + 12( - 3) = - 17\end{lgathered} </p><p></p><p></p><p>$

Therefore the middle terms are - 14 and - 17.