Question

Question 2 (iv)
Verify that each of the following is an AP and then write its next three terms.
a + b, (a + 1) + b, (a + 1) + (b + 1) . . . .

Answer 1

$Here,a_1=a+b,a_2=(a+1)+b,a_3=(a+1)+(b+1)$
$a_2-a_1=(a+1)+b-(a+b)=a+1+b-a=1$
$a_3-a_2=(a+1)+(b+1)-\left[\right(a+1)+b]$
$=a+1+b+1-a-1-b=1$
$\because a_2-a_1=a_3-a_2=1=Commondifference$
Since the difference between successive terms are same, it forms an AP.
The next three terms are,
$a_4=a_1+3d=a+b+3\left(1\right)=(a+2)+(b+1)$
$a_5=a_1+4d=a+b+4\left(1\right)=(a+2)+(b+2)$
$a_6=a_1+5d=a+b+5\left(1\right)=(a+3)+(b+2)$