Answer:
The 22nd term of the arithmetic sequence is 134.
Step-by-step explanation:
Given: The arithmetic sequence where \(a_1=8\) and \(a_9=56\)
We have to find the 22 term of the arithmetic sequence.
Consider the given sequence with \(a_1=8\) and \(a_9=56\)
We know , For a given sequence in an Arithmetic sequence with first term \(a_1\) and common difference d , we have,
\(a_n=a_1+(n-1)d\)
We first find the common difference "d".
\(a_9=56\)
\(a_9=a_1+(9-1)d\)
\(a_1=8\) , we have,
\(56=8+8d\)
Solve for d , we have,
48 = 8d
d = 6
Thus, 22nd term is \(a_{22}=a_1+(22-1)d\)
\(a_{22}=8+21\cdot 6\)
\(a_{22}=134\)
Thus, The 22nd term of the arithmetic sequence is 134.
