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PolarNik [594]
3 years ago
6

Write an explicit formula for a1 = –2, an = an – 1 + 4, n ≥ 2.

Mathematics
1 answer:
iren [92.7K]3 years ago
3 0

The formula given is as follows

a_{1}=-2, a_{n} = a_{n-1}+4, n\geq2

Answer:

a_{n} = 4n - 6

Step-by-step explanation:

Since it is given that n\geq   2

a_{2} = a_{1}+4

a_{3} = a_{2}+4

... and so on...

we substitute a_{1}  to a_{2} , a_{2} to a_{3} and so on.. we will get

a_{3} = a_{2} + 4

   = a_{1} + 4 +4

   = a_{1} + 2(4)

a_{4} = a_{3} + 4

= a_{1} + 2(4) +4

= a_{1} + 3(4)

and the patterns goes on.

We can see from the recursion pattern that

a_{n} = a_{1} + (n-1)(4)

a_{n} = -2 + (n-1)(4)

= -2 + 4n - 4

= 4n - 6

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