✏️ Arithmetic Sequence
[tex] {\Large{\overline{\underline{\sf{\hookrightarrow Answer:}}}}} [/tex]
- [tex] \sf a_n = 2n + 5 [/tex]
Solution:
Given that:
- the first term [tex] \sf a_1 [/tex] = 7
- the common difference [tex] \sf d [/tex] = 2
✎ The common difference can be found by subtracting any term except the first term, by its preceding term. It is given by the formula [tex] \sf d = a_n - a_{n-1} [/tex].
Thus,
- [tex] \sf d = a_n - a_{n-1} \\ \sf d = a_2 - a_1 \\ \sf d = 9 - 7 \\ \sf d = 2 [/tex]
Solve using the formula for the general term of an arithmetic sequence:
[tex] {\large{\boxed{\sf{a_n = a_1 + (n-1)d}}}} [/tex]
- [tex] \sf{a_n = 7 + (n-1)2} [/tex]
- [tex] \sf{a_n = 7 + 2n - 2} [/tex]
- [tex] {\underline{\green{\sf{a_n = 2n + 5}}}} [/tex]
[tex]{\: \:}[/tex]
[tex] {\huge{\overline{\sf{Hope\:It\:Helps}}}} [/tex]
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