Question

Find the 75th term of the arithmetic sequence 13 , 33 , 53 , . . . 13,33,53,...

Answer 1

Question and Answer with Step-by-step explanation:

Find the 75th term of the arithmetic sequence 13 , 33 , 53 , . . .

`a_(n)=a_(1)+d(n-1)`

`a_(1)=13; d=33-13=20`

`a_(n)=20n-7`

`a_(75)=20(75)-7`

`a_(75)=1500-7`

`a_(75)=1493`

Therefore the 75th term of the arithmetic sequence is 1493.

Answer 2

a75=1493

Explanation:

a1=13

a2=33

a3=53

d=a3-a2=a2-a1=20

d=20 and a1=13

an=a1+(n-1)d

a75=13+74*20

a75=13+1480

a75=1493