✏️ Indicated Term in an Arithmetic Sequence
[tex] {\Large{\overline{\underline{\sf{\hookrightarrow Answers:}}}}} [/tex]
- [tex] \sf a_{11} = 45 [/tex]
- [tex] \sf a_{40} = 79x [/tex]
- [tex] \sf a_{16} = \frac{39}{2} [/tex]
- [tex] \sf a_{30} = 88x + 1 [/tex]
Solution:
Here, we use the formula for the general term in an arithmetic sequence:
[tex] {\Large{\boxed{\sf{a_n = a_1 + (n-1)d}}}} [/tex]
1.
Given that:
- [tex] \sf a_{1} [/tex] = 5
- [tex] \sf d [/tex] = 4
- [tex] \sf n [/tex] = 11
Solve:
- [tex] \sf{a_n = a_1 + (n-1)d} [/tex]
- [tex] \sf{a_{11} = 5 + (11-1)4} [/tex]
- [tex] \sf{a_{11} = 5 + (10)4} [/tex]
- [tex] \sf{a_{11} = 5 + 40} [/tex]
- [tex] {\sf \therefore a_{11} = {\boxed{\green{\sf{45}}}}} [/tex]
2.
Given that:
- [tex] \sf a_{1} [/tex] = x
- [tex] \sf d [/tex] = 2x
- [tex] \sf n [/tex] = 40
Solve:
- [tex] \sf{a_n = a_1 + (n-1)d} [/tex]
- [tex] \sf{a_{40} = x + (40-1)2x} [/tex]
- [tex] \sf{a_{40} = x + (39)2x} [/tex]
- [tex] \sf{a_{40} = x + 78x} [/tex]
- [tex] {\sf \therefore a_{40} = {\boxed{\green{\sf{79x}}}}} [/tex]
3.
Given that:
- [tex] \sf a_{1} [/tex] = 12
- [tex] \sf d [/tex] = [tex] \sf \frac{1}{2} [/tex]
- [tex] \sf n [/tex] = 16
Solve:
- [tex] \sf{a_n = a_1 + (n-1)d} [/tex]
- [tex] \sf{a_{16} = 12 + (16-1)\frac{1}{2}} [/tex]
- [tex] \sf{a_{16} = 12 + (15)\frac{1}{2}} [/tex]
- [tex] \sf{a_{16} = 12 + \frac{15}{2} x} [/tex]
- [tex] {\sf \therefore a_{16} = {\boxed{\green{\sf{\frac{39}{2}}}}}} [/tex]
4.
Given that:
- [tex] \sf a_{1} [/tex] = x + 1
- [tex] \sf d [/tex] = 3x
- [tex] \sf n [/tex] = 30
Solve:
- [tex] \sf{a_n = a_1 + (n-1)d} [/tex]
- [tex] \sf{a_{30} = (x + 1) + (30-1)3x} [/tex]
- [tex] \sf{a_{30} = (x + 1) + (29)3x} [/tex]
- [tex] \sf{a_{30} = (x + 1) + 87x} [/tex]
- [tex] {\sf \therefore a_{30} = {\boxed{\green{\sf{88x + 1}}}}} [/tex]
[tex]{\: \:}[/tex]
[tex] {\huge{\overline{\sf{Hope\:It\:Helps}}}} [/tex]
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