An arithmetic sequence has uā = 36 and uāā
= 76.
Calculate the common difference, d.
d =
Answer (1)
To find the common difference d of an arithmetic sequence where u 7 ā = 36 and u 15 ā = 76 , we can use the formula for the n -th term of an arithmetic sequence:
u n ā = u 1 ā + ( n ā 1 ) ā
d
We have two key pieces of information:
u 7 ā = 36
u 15 ā = 76
Let's create two equations using these pieces of information:
Equation 1: u 7 ā = u 1 ā + 6 d = 36
Equation 2: u 15 ā = u 1 ā + 14 d = 76
Now, we can solve these equations to find d , the common difference. First, subtract Equation 1 from Equation 2:
( u 1 ā + 14 d ) ā ( u 1 ā + 6 d ) = 76 ā 36 14 d ā 6 d = 40 8 d = 40 d = 8 40 ā = 5
Thus, the common difference d in the arithmetic sequence is 5 .
