Question

The second term of an arithmetic sequence is 24 and 5th term is 3. Find the first term and the common difference.

Answer 1

we know that
the formula for the arithmetic sequence is
an=a1+d(n-1)

for a2=24 n=2
24=a1+d(2-1)-----> 24=a1+d-----> equation 1

for a5=3 n=5
3=a1+d(5-1)----->3=a1+4d-----> equation 2

multiply equation 1 by -1 and adds to equation 2
-24=-a1-d
3=a1+4d
-------------------
-21=3d
d=-7
24=a1+d-----> 24=a1-7-----> a1=24+7------> a1=31

the answer is
the first term is 31 and the common difference is -7