Question

tolong ya bingung aku soalnya​

Answer 1

Verified answer

بِسْــــــمِ اللّٰهِ الرَّحْمٰنِ الرَّحِيْمَ

..

Jawaban:

[tex] 3. \: \: \rm U_5 = \frac{5}{4} [/tex]

[tex]4. \: \: \rm n = 5[/tex]

Penjelasan dengan langkah-langkah:

Nomor 3

Suatu barisan geometri: 20, -10, 5, ...

Diketahui:

• a = 20
• r = -10 ÷ 20 = -½

Ditanyakan:

• [tex]\rm U_5 [/tex]

Jawab:

[tex] \rm Un = a {r}^{n - 1} [/tex]

[tex]\rm U_5 = 20 \times ( - \frac{1}{2} )^{5 - 1} [/tex]

[tex]\rm U_5 = 20 \times ( - \frac{1}{2} )^{4} [/tex]

[tex]\rm U_5 = 20 \times ( - \frac{1}{16} )[/tex]

[tex]\rm U_5 = \frac{20 \div 4}{16 \div 4} [/tex]

[tex]\rm U_5 = \frac{5}{4} [/tex]

Nomor 4

Diketahui:

• a = 4
• r = ½
• Un = ¼

Ditanyakan:

• n

Jawab:

[tex] \rm Un = a {r}^{n - 1} [/tex]

[tex] \rm \frac{1}{4} = 4 \times ( \frac{1}{2} )^{n - 1} [/tex]

[tex] {2}^{ - 2} = {2}^{2 } \times { ({2}^{ - 1} )}^{n - 1} [/tex]

[tex] {2}^{ - 2} = {2}^{2} \times { 2}^{ - n + 1} [/tex]

[tex] {2}^{ - 2} = {2}^{ - n + 1 + 2} [/tex]

[tex] { \not2}^{ - 2} = { \not2}^{ - n + 3} [/tex]

[tex] - 2 = - n + 3[/tex]

[tex] - 2 - 3 = - n[/tex]

[tex]n = 5[/tex]

Answer 2

Barisan geometri

3). 20, -10, 5,...

[tex]r = \frac{u2}{u1} = - \frac{10}{20} = - \frac{1}{2} \\ \\ aturan = dikali \: - \frac{1}{2} \\ \\ u4 = 5 \times - \frac{1}{2} = - \frac{5}{2} \\ \\ u5 = - \frac{5}{2} \times - \frac{1}{2} = \frac{5}{4} \\ \\ \\ 4).un = {a \times r}^{n - 1} \\ \\ \frac{1}{4} = 4 \times ( { \frac{1}{2} )}^{n - 1} \\ \\ \frac{1}{4 } \times \frac{1}{4} = { {(2}^{ - 1} )}^{n - 1} \\ \\ \frac{1}{16} = {2}^{ - n + 1} \\ \\ {2}^{ - 4} = {2}^{ - n + 1} \\ \\ - 4 = - n + 1 \\ \\ n = 1 + 4 \\ \\ n = 5[/tex]