Math Problem Statement

For the following arithmetic sequence: a) find the specified term a_n and b) find the sum of the terms from a_1 to a_n, inclusive. 7, 9, 11, 13,... find a_12.

Solution

Let's solve for a12a_{12} in the given arithmetic sequence.

Given sequence:

7,9,11,13,7, 9, 11, 13, \dots

  • First term: a1=7a_1 = 7

  • Common difference: d=97=2d = 9 - 7 = 2

  • General formula for the nnth term of an arithmetic sequence: an=a1+(n1)da_n = a_1 + (n - 1) d

  • Plugging in n=12n = 12:

    a12=7+(121)2a_{12} = 7 + (12 - 1) \cdot 2

    a12=7+112a_{12} = 7 + 11 \cdot 2

    a12=7+22=29a_{12} = 7 + 22 = 29

Final Answer:

a12=29a_{12} = 29

Would you like me to also calculate the sum of the first 12 terms?

Here are five related questions for practice:

  1. Find a20a_{20} in the same sequence.
  2. Find the sum of the first 12 terms of this arithmetic sequence.
  3. What is the 50th term of the sequence?
  4. If the sum of the first nn terms is 560, find nn.
  5. Find the sum of the first 100 terms.

Tip: Always identify the first term and common difference before solving arithmetic sequence problems.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Arithmetic Sequence
Sequences and Series
Term Calculation
Sum of Sequence

Formulas

General formula for the nth term of an arithmetic sequence: a_n = a_1 + (n - 1) * d
Sum of first n terms of an arithmetic sequence: S_n = n/2 * (a_1 + a_n)

Theorems

Properties of Arithmetic Sequences

Suitable Grade Level

Grades 7-9