The 3rd and 12th terms of an arithmetic progression are 12 and -24 respectively. What is the 50th term?
what is the product of 23 and 45.
To find the 50th term of an arithmetic progression, we need to determine the common difference between terms first.
The common difference (d) can be calculated by taking the difference between any two consecutive terms in the arithmetic progression. In this case, we can use the given 3rd and 12th terms, which are 12 and -24 respectively.
To find the common difference:
d = (12 - (-24)) / (12th term number - 3rd term number)
= (12 + 24) / (12 - 3)
= 36 / 9
= 4
Now that we have the common difference (d = 4), we can calculate the 50th term using the formula for the nth term of an arithmetic progression:
an = a1 + (n - 1) * d
where:
an = nth term
a1 = first term
n = term number
d = common difference
In this case, the first term (a1) is given as 12.
To find the 50th term:
a50 = a1 + (50 - 1) * d
= 12 + (49) * 4
= 12 + 196
= 208
Therefore, the 50th term of the arithmetic progression is 208.
a+2d=12
a+11d=-24
subtract them
9d = -36
d = -4
then a-8=12
a=20
term(50) = a+49d
= ...