The second term of an arithmetic progression is 50 and the 5th term is 65.calculate the value of the 40th term
To find the value of the 40th term in an arithmetic progression, we need to determine the common difference (d) between consecutive terms.
In an arithmetic progression, the nth term (Tn) can be found using the formula:
Tn = a + (n - 1) * d
Where:
Tn = nth term
a = first term
n = term number
d = common difference
Given that the second term (T2) is 50, we can write it as:
T2 = a + (2 - 1) * d
50 = a + d
Similarly, the fifth term (T5) is 65:
T5 = a + (5 - 1) * d
65 = a + 4d
Now, we have two equations:
50 = a + d
65 = a + 4d
By solving these two equations simultaneously, we can find the values of 'a' and 'd'.
a+d = 50
a + 4d=65
subtract them
3d = 15
d = 5
then a+5=50
a=45
term40 = a + 39d = 45 + 39(5) = 240