Question

For an arithmetic sequence that sums to 1485 it is known that the first term equals 6 and the last term equals 93 algebraically determine the number of terms summed in this series

Answer 1

For an arithmetic sequence that sums to 1485 with a first term of 6 and a last term of 93, there are 30 terms summed in this series.

Step-by-step explanation:

To find the number of terms summed in the arithmetic sequence, we can use the formula for the sum of an arithmetic series.

The formula is given by S = (n/2)(a + l), where S is the sum, n is the number of terms, a is the first term, and l is the last term.

In this case, we are given that S = 1485, a = 6, and l = 93. Plugging these values into the formula, we get 1485 = (n/2)(6 + 93).

Simplifying the equation further, we have 1485 = (n/2)(99).

Multiplying both sides of the equation by 2, we get 2970 = n(99).

Dividing both sides of the equation by 99, we finally arrive at n = 30.