Question

In an arithmetic​ sequence, the nth term an is given by the formula An=a1+(n−1)d​, where a1

is the first term and d is the common difference.​ Similarly, in a geometric​ sequence, the nth term is given by an=a1•rn−1.

Here r is the common ratio. Use these formulas to determine the indicated term in the given sequence.

The 30th term of 1​, 4​, 7​, 10​,...

Answer 1

Answer:

$a_{30} = 88$

Step-by-step explanation:

In this question we are given a sequence:

1, 4, 7, 10,...

If we closely examine this series it is an arithmetic progression.

An arithmetic progression is of the form $a, a+d, a+2d, a+3d, ...$, where a is the first term of the series and d is the common difference.

The $n^{th}$ term of the series is given by the formula:

$a_n = a + (n-1)d$

The $30^{th}$ term of the given series is:

$a_{30} = a + (29)d = 1 + (29)3 = 88$