Question

50=n/2[10+(n-1) (-1/4)]​

Answer 1

Answer:

$S_{n} = \frac{n}{2} [ 2a + (n - 1)d ]$

$S_{n} = 50$

$a = 5$

$d = \frac{ - 1}{4}$

$50 = \frac{n}{2}[10 + (n - 1)( \frac{ - 1}{4}]$

$50 = \frac{n}{2} \times 2[5 + (n - 1)( \frac{ - 1}{8} )]$

$50 = n[5 - \frac{ n}{8} + \frac{1}{8}]$

$50 = 5n - \frac{ {n}^{2} }{8} + \frac{n}{8}$

$50 = \frac{40n - {n}^{2} + n }{8}$

Multiplying by 8 on both sides

$400 = 41n - {n}^{2}$

${n}^{2} - 41n + 400 = 0$

$(n-16)(n-25) = 0$

$n = 25 \: or \: 16$

Answer 2

Answer:

$</p><p></p><p>S_{n} = \frac{n}{2} [ 2a + (n - 1)d ]Sn=2n[2a+(n−1)d] \\ </p><p></p><p>S_{n} = 50Sn=50 \\ </p><p></p><p>a = 5a=5 \\ </p><p></p><p>d = \frac{ - 1}{4}d=4−1 \\ </p><p></p><p>50 = \frac{n}{2}[10 + (n - 1)( \frac{ - 1}{4}]50=2n[10+(n−1)(4−1] \\ </p><p></p><p>50 = \frac{n}{2} \times 2[5 + (n - 1)( \frac{ - 1}{8} )]50=2n×2[5+(n−1)(8−1)] \\ </p><p></p><p>50 = n[5 - \frac{ n}{8} + \frac{1}{8}]50=n[5−8n+81] \\ </p><p></p><p>50 = 5n - \frac{ {n}^{2} }{8} + \frac{n}{8}50=5n−8n2+8n \\ </p><p></p><p>50 = \frac{40n - {n}^{2} + n }{8}50=840n−n2+n \\ </p><p></p><p>Multiplying \: by \: 8 \: on \: both \: sides</p><p></p><p>400 = 41n - {n}^{2}400=41n−n2 \\ </p><p></p><p>{n}^{2} - 41n + 400 = 0n2−41n+400=0 \\ </p><p></p><p>(n-16)(n-25) = 0 \\ </p><p></p><p>n = 25 \: or \: 16n=25or16</p><p></p><p>$