Question

The sum of 5th and 7th term of an ap is 52 and the 10th term is 46 find the

Answer 1

Answer:

Let the first term and common difference of AP are a and d, respectively.

According to the question,

a5 + a7 = 52 and a10 = 46

⇒ a + (5-1)d + a + (7-1)d = 52 [∵an = a + (n-1)d]

and a + (10-1)d = 46

⇒ a + 4d + a + 6d = 52  

and a + 9d = 46

⇒ 2a + 10d = 52  

and a + 9d = 46

⇒ a + 5d = 26 ...(i)

a + 9d = 46

On subtracting Eq.(i) from Eq.(ii),we get

4d = 20 ⇒ d = 5

From Eq.(i),  a = 26 - 5(5) = 1

So, required AP is a,a+d,a+2d,a+3d,...i.e., 1,1 + 5,1 + 2(5), 1 + 3(5),... i.e.,

1,6,11,16,...

Step-by-step explanation: