Identify the 35th term of an arithmetic sequence where a1= -7 and a18=95
To identify the 35th term of an arithmetic sequence, we need to find the common difference (d) first.
The formula for the nth term (an) of an arithmetic sequence is given by:
an = a1 + (n - 1) * d,
where a1 represents the first term, n is the term number, and d represents the common difference.
We are given that a1 = -7 and a18 = 95.
Substituting these values into the formula, we can find the value of a18:
95 = -7 + (18 - 1) * d.
Simplifying the equation:
95 = -7 + 17d.
102 = 17d.
d = 6.
Now that we have the common difference, we can find the 35th term (a35). Substituting the values into the formula:
a35 = -7 + (35 - 1) * 6.
Simplifying the equation:
a35 = -7 + 34 * 6.
a35 = -7 + 204.
a35 = 197.
Therefore, the 35th term of the arithmetic sequence is 197.
there are 17 differences from a1 to a18
the total difference between the terms is ... a18 - a1
so the difference between two consecutive terms is ... (a18 - a1) / 17
there are 34 differences between a1 and a35