MATH SOLVE

3 months ago

Q:
# Use sigma notation to represent the sum of the first eight terms of the following sequence: 4, 7, 10, … the summation from n equals 1 to 8 of negative 4 plus 3 times n the summation from n equals 1 to 8 of negative 1 plus 3 times n the summation from n equals 1 to 8 of 1 plus 3 times n the summation from n equals 1 to 8 of 4 plus 3 times n

Accepted Solution

A:

Answer:" the summation from n equals 1 to 8 of 1 plus 3 times n " ⇒ 3rd answerStep-by-step explanation:The sequence is : 4 , 7 , 10 , ........∵ 7 - 4 = 3∵ 10 - 7 = 3∴ The sequence is an arithmetic sequence, where the first term is 4 and the constant difference is 3∵ The rule of the arithmetic sequence is [tex]a_{n}= a_{1}+(n-1)d[/tex],where [tex]a_{1}[/tex] is the first term, d is the constant difference andn is the position of the term in the sequence∵ [tex]a_{1}=4[/tex] ∵ d = 3∴ [tex]a_{n}= 4+(n-1)3[/tex]∴ [tex]a_{n}= 4+3n-3[/tex]∴ [tex]a_{n}= 1+3n[/tex]The segma notation is:∑[tex]\left \ {{n=8} \atop {n=1}} \right.[/tex] (1 + 3n)It means " the summation from n equals 1 to 8 of 1 plus 3 times n "