Question

find the 52nd term and the explicit formula

1. 37, 47, 57, 67, ...

d=
explicit formula:
52nd term:

Explanation:

Step1: Calculate common difference $d$

Subtract consecutive terms: $d = 47 - 37 = 10$

Step2: Write explicit formula

Use arithmetic sequence formula $a_n = a_1 + (n-1)d$, where $a_1=37$, $d=10$:
$a_n = 37 + (n-1) \times 10$
Simplify: $a_n = 10n + 27$

Step3: Find 52nd term

Substitute $n=52$ into explicit formula:
$a_{52} = 10(52) + 27$

Answer:

$d=10$
explicit formula: $a_n = 10n + 27$
52nd term: $547$