What is "given the geometric sequence where a1 = 1 and the common ratio is 6?

In a geometric sequence, each term after the first is obtained by multiplying the preceding term by a fixed factor, called the common ratio. In this case, a1 (the first term) is given as 1 and the common ratio is given as 6. Therefore, the terms in the sequence are:

a1 = 1 a2 = 6a1 = 6(1) = 6 a3 = 6a2 = 6(6) = 36 a4 = 6a3 = 6(36) = 216 a5 = 6a4 = 6(216) = 1296 ...

The general formula for the nth term (an) in a geometric sequence with first term a1 and common ratio r is:

an = a1 * r^(n-1)

In this case, we have a1 = 1 and r = 6, so the formula becomes:

an = 1 * 6^(n-1)

Using this formula, we can find any term in the sequence by plugging in the appropriate value of n. For example, the 10th term would be:

a10 = 1 * 6^(10-1) = 1 * 6^9 = 10,077,696