The 9th term of an AP is -32 and the sum of its 11th and 13th terms is

1.	The 9th term of an AP is -32 and the sum of its 11th and 13th terms is -94. Find the common difference of the AP.
Answer» Let a be the first term and d be the common difference of an AP. nth term = a_n = a + (n – 1)d Given: 9th term of an AP is -32 and the sum of its 11th and 13th terms is -94 Now, a₉ = a + 8d = -32 …(1) a₁₁ = a + 10d a₁₃ = a + 12d Sum of 11th and 13th terms: a₁₁ + a₁₃ = a + 10d + a + 12d -94 = 2a + 22d or a + 11d =-47 …(2) Subtracting (1) from (2) , we have 3d = -47 + 32 = -15 or d = -5 Common difference is -5.

The 9th term of an AP is -32 and the sum of its 11th and 13th terms is -94. Find the common difference of the AP.

Answer»

Let a be the first term and d be the common difference of an AP.

nth term = a_n = a + (n – 1)d

Given: 9th term of an AP is -32 and the sum of its 11th and 13th terms is -94

Now,

a₉ = a + 8d = -32 …(1)

a₁₁ = a + 10d

a₁₃ = a + 12d

Sum of 11th and 13th terms:

a₁₁ + a₁₃ = a + 10d + a + 12d

-94 = 2a + 22d

or a + 11d =-47 …(2)

Subtracting (1) from (2) , we have

3d = -47 + 32 = -15

or d = -5

Common difference is -5.