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Find an for each of arithmetic sequence. 1. a1=5, d=4,n=11
2. a1=x, d=2x, n=40
3. a1=12, d=½, n=16
4. a1=x+1, d=3x, n=30​

Sagot :

RhoZetaidn

✏️ Indicated Term in an Arithmetic Sequence

[tex] {\Large{\overline{\underline{\sf{\hookrightarrow Answers:}}}}} [/tex]

  1. [tex] \sf a_{11} = 45 [/tex]
  2. [tex] \sf a_{40} = 79x [/tex]
  3. [tex] \sf a_{16} = \frac{39}{2} [/tex]
  4. [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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