Question

What is Rational and Irrational numbers​

Answer 1

Given

If the sum of of 6 terms of an A.p is 36 and that of 10 terms of an A.p is 100 .

Find out

Find the sum of nth term

Solution

S6 = 36

As we know that

→ Sn = n/2[2a + (n - 1)d]

→ S6 = 6/2[2a + (6 - 1)d]

→ 36 = 3[2a + 5d]

→ 36/3 = 2a + 5d

→ 2a + 5d = 12 ----(i)

S10 = 100

→ S10 = 10/2[2a + (10 - 1)d]

→ 100 = 5[2a + 9d]

→ 100/5 = 2a + 9d

→ 2a + 9d = 20 -----(ii)

Subtract both the equation

→ (2a + 5d) - (2a + 9d) = 12 - 20

→ 2a + 5d - 2a - 9d = -8

→ - 4d = - 8

→ d = 8/4 = 2

Put the value of d in Equation (i)

→ 2a + 5d = 12

→ 2a + 5 × 2 = 12

→ 2a + 10 = 12

→ 2a = 12 - 10

→ 2a = 2

→ a = 1

Now the sum of nth term

Common Difference (d) = 2

First term (a) = 1

→ Sn = n/2[2a + (n - 1)d]

→ Sn = n/2[2 × 1 + (n - 1)2]

→ Sn = n/2[2 + 2n - 2]

→ Sn = n/2 × 2n

→ Sn = n²

Hence, the sum of nth term n²

Answer 2

• Answer :-

→ Rational number → The number in form of p/q where p and q are integer and q ≠ 0

• Example = ⅔, ¾ ...etc

→ Irrational number → The number that isn't in the form of p/q.

• Example = √2, √3... etc