Find the first term and common difference of the A. P.s.Its 5th and 10th
term are
86 and 146
5d = 146-86
now use d to find a, since
a+4d = 86
To find the first term and common difference of an arithmetic progression (A.P.), we can use the formulas:
nth term of A.P. = a + (n - 1)d
where:
- nth term is the term number you want to find,
- a is the first term of the A.P.,
- n is the term number,
- d is the common difference.
Let's use these formulas to find the first term and common difference of the A.P. with the 5th and 10th terms given as 86 and 146, respectively.
Step 1: Finding the common difference (d):
Using the formula for the nth term, we have:
10th term = a + (10 - 1)d = a + 9d
Substituting the given value: 146 = a + 9d
Step 2: Finding the first term (a):
Using the formula for the nth term, we have:
5th term = a + (5 - 1)d = a + 4d
Substituting the given value: 86 = a + 4d.
Now, we have a system of two equations:
146 = a + 9d
86 = a + 4d
To solve this system, we can subtract the second equation from the first equation:
(146 - 86) = (a + 9d - a - 4d)
60 = 5d
Dividing by 5, we find:
d = 12
Now, substitute the value of d into one of the equations to find the first term a:
86 = a + 4(12)
86 = a + 48
a = 86 - 48
a = 38
Therefore, the first term (a) of the arithmetic progression is 38 and the common difference (d) is 12.