I can't solve this one:
The second term of an arithmetic sequence is 24 and the fifth term is 3.Find the first term and the common difference.
How could I get the answers if there's only two given numbers?
2nd term = 24
5th term = 3
24-3 = 21
5-2 = 3
21/3 = 7
common difference = -7 since the terms are decreasing
so to find the first term, subtract -7 from 24
so the first term is equal to 31
traditional method:
a+d = 24
a+4d = 3
subtract them:
3d = -21
d = -7
sub into a+d = 24
a - 7 = 24
a = 31
first term is 31, commond difference is -7
how many terms are there in an arithmetic sequence those first term is -4 common difference 2 and last term is 24?
The second term if can arithmetic sequence is 24 and the fifth term is 3 find the first term and common difference
To find the first term (a) and the common difference (d) of an arithmetic sequence, you will need at least two known terms. In this case, we have the second term (a2 = 24) and the fifth term (a5 = 3).
To solve for the first term (a):
1. Use the formula for the nth term of an arithmetic sequence: an = a + (n - 1)d.
Plug in the known values for a5 and d:
a5 = a + 4d (since the fifth term has the index n = 5)
2. Substitute the given value for a5 (3) into the equation:
3 = a + 4d
To solve for the common difference (d):
3. Use the formula for the second term (a2) in relation to the first term (a) and the common difference (d):
Plug in the given value for a2 (24) into the equation:
a2 = a + d
Solving the equations simultaneously will yield the values of a and d.