Question

Given: 20, 26, 32, 38, 44, ...

Write the equation (formula) for the given Arithmetic Sequence.
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Find the 15th term of this Arithmetic Sequence.
a15=

Answer 1

see explanation

Explanation:

the nth term of an arithmetic sequence is

`a_(n)` = a₁ + d(n - 1)

a₁ is the first term, d the common difference , n the term number

the common difference d is the difference between consecutive terms in the sequence, then

d = a₂ - a₁ = a₃ - a₂ = ..... =
`a_(n)` -
`a_(n-1)`

given the sequence

20 , 26 , 32 , 38 , 44 , .....

d = a₂ - a₁ = 26 - 20 = 6

`a_(n)` = 20 + 6(n - 1) = 20 + 6n - 6 = 6n + 14

the formula for the sequence is then

`a_(n)` = 6n + 14

to find the 15th term , substitute n = 15 into the formula

a₁₅ = 6(15) + 14 = 90 + 14 = 104