Question

Find 11th term of an ap
10.0 , 10.5 , 11.0 , 11.5

Answer 1

Dear student,
Given A.P is 10.0,10.5,11.0,11.5,.....
first term of this A.P is a_{​​​​​​1}​ =10.0
second term of this A.P is a_{​​​​​​2}​ =10.5
common difference of an A.P is given by (i.e.,d=a_{​​​​​​n+1} ​ −a_n ​)
​​​​​​
putting n=1 in above equation,
d=a_{​​​​​​2} ​ −a₁ ​ =10.5−10=0.5
hence common difference for this A.P is d=0.5
the nth term of an A.P is given by.
a_n​ =a_{​​​​​​1} ​ +(n−1)d
⟹a_n ​=10+(n−1)(0.5)
⟹a_n ​ =10+0.5n−0.5
⟹a_n ​ =9.5+0.5n...eq(1)
for finding 11th term (a 11 ​ )of this A.P
put n=11 in above eq(1)
⟹a₁₁ ​ =9.5+0.5×11
⟹a₁₁ ​ =9.5+5.5
⟹a₁₁ ​ =15.0
Regards.