The 41th term of the arithmetic sequence is 66.
Arithmetic sequences are those that contain these patterns. The difference between successive terms in an arithmetic series is constant. Because the difference between consecutive words is always two, the sequence 3, 5, 7, and 9 is an example of arithmetic.
[tex]a_{n}=a_{1}+(n-1)d[/tex]
[tex]a_n[/tex] = the nᵗʰ term in the sequence.
[tex]a_1[/tex] = the first term in the sequence.
d = the common difference between terms.
Finding arithmetic sequence for the nth term:
aₙ = a₁ + (n-1)d
d = the common difference
a₇ = a₁ + (7-1)d
34 = 5 + 6d
29 = 6d
d = 29/6
Now ,
Finding the 41st term of the arithmetic sequence.
a₄₁ = a₁ + (n-1)d
= 5 + (41-1)d
= 5 + 40d
= 5 + 40(29/6)
= (198)* 1/3
= 66
The 41th term of the arithmetic sequence is 66.
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