MATH SOLVE

3 months ago

Q:
# What is the rule for the sequence corresponding to this series? –4 + –7 + –10 + –13

Accepted Solution

A:

Answer:The rule or the sequence is : an = -3n - 1Step-by-step explanation:* Lets look to the terms of the sequence -4 , -7 , -10 , -13- The difference between each two consecutive terms is: -7 - -4 = -3 , -10 - -7 = -3 . -13 - -10 = -3 ∴ It is an arithmetic sequence* because we add a constant value to each term to find the second term- That means a1 = a , a2 = a + d , a3 = a + 2d , ............* The rule of any term of the arithmetic sequence is;- an = a + (n - 1) d , where a is the first term , d is the constant difference and n is the position of the number in the sequence ∵ a = -4 and d = -3∴ The rule of any term in this sequence is:* an = -4 + (n - 1)(-3) * Lets simplify the formula∴ an = -4 + -3n + 3∴ an = -3n - 1* The rule or the sequence is : an = -3n - 1