Math Problem Statement

Find the sum of the first 8 terms of the following sequence. Round to the nearest hundredth if necessary. 75, comma, 91, point, 5, comma, 111, point, 6, 3, comma, point, point, . 75,91.5,111.63,

Solution

The given sequence appears to follow a pattern, and it looks like an arithmetic sequence. The terms given are:

  • a1=75a_1 = 75
  • a2=91.5a_2 = 91.5
  • a3=111.63a_3 = 111.63

To verify if this is an arithmetic sequence, we need to check if the difference between consecutive terms is constant:

  1. Difference between a2a_2 and a1a_1: d=91.575=16.5d = 91.5 - 75 = 16.5

  2. Difference between a3a_3 and a2a_2: d=111.6391.5=20.13d = 111.63 - 91.5 = 20.13

Since the differences are not the same, this isn't an arithmetic sequence. This suggests that the sequence may follow a different rule.

It is possible that the sequence follows some other pattern, but to find the sum of the first 8 terms, I'll need more information on how the sequence progresses beyond the third term.

Could you provide more terms or specify the type of sequence?

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Math Problem Analysis

Mathematical Concepts

Sequences
Arithmetic Sequences
Sum of Terms

Formulas

Sum of arithmetic sequence: S_n = n/2 * (2a + (n-1)d)

Theorems

Arithmetic progression theorem

Suitable Grade Level

Grades 9-11