In the following A.P.'s, find the missing terms in the boxes.

Explanation

(i) `2, square , 26`
`rArr 2,x,26` are in A.P. (say)
`rArr x=(2+26)/(2)=14`
(ii)`square, 13,square,3`
`rArr x,13,y,3` are in A.P. (say)
`:. Y=(13+3)/(2)=8`
and `(x+y)/(2)=13`
`rArr x+y=26`
`rArr x+8=26`
`rArr x=18`
`rArr x=18,y=8`
(ii) `5,square,square,9(1)/(2)`
`rArr 5,x,y,(19)/(2)` are in A.P.. (say)
Here, a=5
and `a_(4)=(19)/(2)`
`rArr 5+3d=(19)/(2)`
`rArr 3d=(19)/(2)-5=(9)/(2) rArr d=(3)/(2)`
`:. x=5+d=5+(3)/(2)=(13)/(2)`
and `y=5+2d=5+2xx(3)/(2)=8`
`:. x=(13)/(2),y=8`
(iv) `-4square,square,square,square,6`
`rArr -4,p,q,r,s,6` are in A.P. (say)
Here, `a=-4` and `a_(6)=6`
`rArr -4+5d=6`
`rArr 5d=10 rArr d=2`
`:. p=-4+d=-4+2=-2`
`q=-4+2d=-4+2xx2=0`
`r=-4+3d=-4+3xx2=2`
`s=-4+4d=-4+4xx2=4`
`p=-2,q=0,r=2,s=4`
(v)`square,38,square,square,square,-22`
`rArr p, 38,q,r,s,-22 ` are in A.P. (say)
Here, `a_(2)=38`
`rArr p+d=38 " " ...(1)`
and `a_(6)=-22`
`rArr p+5d=-22 " " ...(2) `
Subtract equation (1) from (2), we get
`{:(p+5d=""-22),(underset(-)" "punderset(-)+d=""underset(-)38),(bar(" "4d=-60" ")):}`
`rArr" " d=-15`
put d=-15 in equation (1), we get
p+(-15)=38
`rArr p=53`
`:. q=38+d=38+(-15)=23`
`r=q+d=23+(-15)=8`
`s=r+d=8+(-15)=-7`
`:. p=53, q=23, r=8, s=-7`