What is a1 if a33 is equal to -2p and a74 = 26p?
Our topic is arithmetic series and sequence. Thanks.
To find the value of a1, we need to understand the concept of an arithmetic series/sequence and how it is represented.
In an arithmetic sequence, each term is obtained by adding a constant difference (d) to the preceding term. The first term, a1, is denoted as the starting term, and the next term is a2, then a3, and so on.
In this case, we are given that a33 equals -2p and a74 equals 26p. Since the difference between two consecutive terms is constant, we can find the term-to-term difference by subtracting the two terms:
d = a74 - a33 = 26p - (-2p) = 28p
Now that we have the difference, we can find a1 using the formula for the nth term of an arithmetic sequence:
a1 = a(n) - (n - 1)d
Since a33 is the 33rd term, we can substitute the values:
a1 = a33 - (33 - 1)d = -2p - 32d = -2p - 32(28p) = -2p - 896p = -898p
Therefore, a1 is equal to -898p.