Question

1)

Find the explicit formula that defines the sequenc
Consider the sequences
6,810,-)
2)
Find the 130th term of the sequence
A
202
D
262

Answer 1

see explanation

Explanation:

Note the common difference d between consecutive terms of the sequence

8 - 6 = 10 - 8 = 2

This indicates that the sequence is arithmetic with n th term

`a_(n)` = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = 6 and d = 2, thus

`a_(n)` = 6 + 2(n - 1) = 6 + 2n - 2 = 2n + 4 ← explicit formula

Hence

`a_(130)` = (2 × 130) + 4 = 260 + 4 = 264