Answer:
95th term
Step-by-step explanation:
the nth term of an AP is
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
here a₁ = 2 and d = a₂ - a₁ = 8 - 2 = 6 , then
[tex]a_{n}[/tex] = 2 + 6(n - 1) = 2 + 6n - 6 = 6n - 4
the 60th term is then
a₆₀ = 6(60) - 4 = 360 - 4 = 356
so 210 more than a₆₀ = 356 + 210 = 566
now equate [tex]a_{n}[/tex] to 566 and solve for n
6n - 4 = 566 ( add 4 to both sides )
6n = 570 ( divide both sides by 6 )
n = 95
Answer:
95th term.
Step-by-step explanation:
The sequence of 2, 8, 14, 20 . . . can be predicted by adding 6 to each successive term. This can be written as 6n+2, where n starts at 0 for the first term.
n Value (6n+2)
0 2
1 8
2 14
3 20
4 26
60 362
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We want to know what term is 210 more than 362. (362+ 210) = 572
We can solve by using the equation in reverse and solving for n:
(6n+2) = 572
6n = 570
n = 95
The 95th term (572) is greater than the 60th term (362) by 210.
