Question

Find 11th term of the A.P. $10.0,10.5,11.0,11.5,......$

Answer 1

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

$d=a_2-a_1=10.5-10=0.5$

hence common difference for this A.P is $d=0.5$

the nth term of an A.P is given by.

$a_n=a_1+(n-1)d$

$⟹a_n=10+(n-1)\left(0.5\right)$

$⟹a_n=10+0.5n-0.5$

$⟹a_n=9.5+0.5n...eq\left(1\right)$

for finding 11th term $\left(a_{11}\right)$of this A.P put n=11 in above eq(1)

$⟹a_{11}=9.5+0.5\times 11$

$⟹a_{11}=9.5+5.5$

$⟹a_{11}=15.0$