The sum of the 5th &6th terms of ap is 36& the sum of the 8th &9th terms is 48 find the first 3terms of an ap
Answers
Answer:
Let a be the first term of the Arithmetic progression, d be the common difference of the Arithmetic progression.
5th term = a + 4d
9th term = a + 8d.
According to the question,
The sum of 5th and 9th terms of AP is 40.
So, ( a + 4d)+( a + 8d) = 40
2a + 12 d = 40
a + 6d = 20
8th term = a + 7d
14th term = a + 13d
According to the question,
The sum of 8th and 14th terms of AP is 64
So, a + 7d + a + 13 d = 64
2a + 20 d = 64
a + 10d = 32
We have two equations in two variables, We shall now solve them.
a + 10d = 32
a + 6d = 20
We get, 4d = 12, d = 3 on subtracting both the equations.
Now, a = 20 - 6d = 20 - 6(3) = 2
Sum of n terms of an A.P is defined,
We need sum of first 20 terms, so n = 20
Therefore, The sum of first 20 terms is 610
Step-by-step explanation: