If 23rd and 24th terms of an A.P. be 42 and 312 respectively, then its 37th term is:
3822
To find the 37th term of an arithmetic progression (A.P.), we first identify the given terms and use the formula for the nth term of an A.P.: \(a_n = a + (n-1) \cdot d\), where \(a\) is the first term and \(d\) is the common difference.
Given:
- 23rd term: \(a + 22d = 42\)
- 24th term: \(a + 23d = 312\)
We have two equations:
- \(a + 22d = 42\)
- \(a + 23d = 312\)
Subtracting the first equation from the second to find \(d\):
\((a + 23d) - (a + 22d) = 312 - 42\)
\(d = 270\)
Substitute \(d = 270\) back into the first equation to find \(a\):
\(a + 22 \cdot 270 = 42\)
\(a + 5940 = 42\)
\(a = 42 - 5940 = -5898\)
Now, find the 37th term:
\(a + 36d = -5898 + 36 \cdot 270\)
\(= -5898 + 9720 = 3822\)
Therefore, the 37th term of the A.P. is 3822.
Important Questions from Arithmetic Progression
What is the arithmetic mean of first 8 multiples of 13?
The average of five consecutive odd natural numbers is 27. The product of the first and fifth number is:
Find the sum of all the numbers between 100 to 200 which are divisible by 12.
In a garden, there are 6 daisy plants the first year. Each year, a gardener adds 3 new daisy plants the first year and loses 2 each year. He has 26 jasmine plants the first year and loses 2 each year. When will the number of daisy plants equal the number of jasmine plants after the first year?
The first and last terms of an A.P. are 18 and 48. If the sum of its terms is 396, then the number of terms will be?
