Question

# The 4th term of an AP is 4 and the 8th term is 22 what is the 1st term?

Sequences
The 4th term of an AP is 4 and the 8th term is 22 what is the 1st term?

2021-05-15
The nnth term of an arithemtic progression with a1 as the first term and dd as the common difference is given by:
an=a1+(n−1)d
Using the 4th term, we write one equation:
a4=a1+(4−1)d
4=a1+3d(1)
Using the 8th term, we write one equation:
a8=a1+(8−1)d
22=a1+7d(2)
Subtract each side of (1) and (2) and solve for dd:
−18=−4d
4.5=d
Solve for a1 using (1):
4=a1+3(4.5)
4=a1+13.5
−9.5=a1
The first term is −9.5.
2021-08-11

Explanation