Question

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 ​

Answer 1

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: