An important and exam oriented question from arithmetic progression chapter in which we have been asked to find the common difference, if the 9th term of an AP is -32 and the sum of the 11th and 13th terms is -94.
RS Aggarwal, Class 10, chapter 5A, question no 30
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.