Question

Find the value of the middle term of the following AP: −6, −2, 2, ……, 58.
OR
Determine the AP whose fourth term is 18 and the differences of the ninth term from the fifteenth term is 30.

Answer 1

first term ,a = -6 , common difference d = -2+6= 4
last term = 58
-6 + (n-1)4 =58
n-1 = 64/4
n-1 = 16
total no. of terms,n = 17
middle term is 9th term .
then 9th term, a9 = -6 + (9-1)4
= -6 + 32 = 26

OR

4th term= 18, a +3d = 18 ......eqn 1.
also, diff. of 15th & 9th term
a15 - a9 = 30
(a + 14d) - ( a + 8d) = 30
a + 14d - a - 8d = 30
6d = 30
d = 5
then put in eqn 1.
a + 3×5 = 18
a = 3
A.P becomes
3,8,13,18....