s1859752 s1859752
  • 14-04-2020
  • Mathematics
contestada

Find the 75th term of the arithmetic sequence -17, -13, -9, ...−17,−13,−9,...

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LammettHash
LammettHash LammettHash
  • 14-04-2020

The terms in this sequence are 4 units apart. If [tex]a_1=-17[/tex] is the first term in the sequence, then the next few terms are obtained by adding 4 to the preceding term:

[tex]a_2=a_1+4=-13[/tex]

[tex]a_3=a_2+4=a_1+2\cdot4=-9[/tex]

[tex]a_4=a_3+4=a_1+3\cdot4=-5[/tex]

and so on, leading up to the [tex]n[/tex]th term

[tex]a_n=a_{n-1}+4=a_{n-2}+2\cdot4=\cdots=a_1+(n-1)\cdot4[/tex]

[tex]\implies a_n=-17+4(n-1)=4n-21[/tex]

Then the 75th term in the sequence is

[tex]a_{75}=4\cdot75-21=279[/tex]

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