ARITHMETIC SEQUENCE

[tex]=======================[/tex]

[tex]\begin{gathered}{\underline{\huge \mathbb{D} {\large \mathrm {IRECTION : }}}} \\\end{gathered} [/tex]

• Write the general term of each arithmetic sequence by completing each steps given.

[tex]=======================[/tex]

[tex]\begin{gathered}{\underline{\huge \mathbb{A} {\large \mathrm {NSWER \: \: (1) : }}}} \\\end{gathered} [/tex]

[tex] \qquad \qquad \large \bold{ \: \: a_{n} = 8n + 1} \\ [/tex]

[tex]=======================[/tex]

[tex]\begin{gathered}{\underline{\huge \mathbb{S} {\large \mathrm {OLUTION \: \: (1) : }}}} \\\end{gathered}[/tex]

To find the general terms of each arithmetic sequence we must fill in the blank and follow the step to get the general term of a arithmetic sequence.

[tex] \\ [/tex]

[tex] \sf{Given \: that:} \\ [/tex]

• [tex] \bold{a_{1} = 9} \\ [/tex]
• [tex] \bold{n = 8} \\ [/tex]

As of, to identify the blank steps we must insert the indicated values as given above:

[tex]\sf\implies\: a_n = a_1 + (n -1)d \\ [/tex]

[tex]\sf\implies\: a_n = \underline{ \: \: 9 \: \: } + (n -1)8 \\ [/tex]

[tex]\sf\implies\: a_n = 9 + \underline{ \: \: 8n \: \: } -8 \\ [/tex]

[tex]\sf\implies\: a_n = \underline{\:\:8n \:\:} + 9-8 \\\\ [/tex]

[tex] \qquad\sf\implies\: \bold{ General \: Term : \:\: \boxed{ \bold{\green{a_n = 8n + 1}}}} \\ [/tex]

[tex]=======================[/tex]

[tex]\begin{gathered}{\underline{\huge \mathbb{A} {\large \mathrm {NSWER \: \: (2) : }}}} \\\end{gathered} [/tex]

[tex] \qquad \qquad \large \bold{ \: \: a_n = -6n + 51} \\ [/tex]

[tex]=======================[/tex]

[tex]\begin{gathered}{\underline{\huge \mathbb{S} {\large \mathrm {OLUTION \: \: (2) : }}}} \\\end{gathered}[/tex]

To find the general terms of each arithmetic sequence we must fill in the blank and follow the step to get the general term of a arithmetic sequence.

[tex] \\ [/tex]

[tex] \sf{Given \: that:} \\ [/tex]

• [tex] \bold{a_{1} = 45} \\ [/tex]
• [tex] \bold{n = - 6} \\ [/tex]

As of, to identify the blank steps we must insert the indicated values as given above:

[tex]\sf\implies\: a_n = a_1 + (n -1)d \\ [/tex]

[tex]\sf\implies\: a_n = \underline{ \: \: 45 \: \: } + (n -1) \underline{ \: \: - 6 \: \: } \\ [/tex]

[tex]\sf\implies\: a_n = \underline{ \: \: 45 \: \: } + \underline{ \: \: (- 6n) \: \: } + \underline{ \: \: 6 \: \: } \\ [/tex]

[tex]\sf\implies\: a_n = \underline{ \: \: - 6n\: \: } + 45\ + \underline{ \: \: 6 \: \: } \\ \\ [/tex]

[tex] \qquad\sf\implies\: \bold{ General \: Term : \: \: \boxed{ \bold{\green{a_n = - 6n + 51}}}} \\ [/tex]

[tex]=======================[/tex]