Question

A few boxes are arranged with the help of numbers on
them in ascending
order and it is given that these
numbers are in AP. If the sum of numbers on
the first 4
boxes is 24 and the difference between the numbers on
consecutive boxes is 2. What is the number on the 5th
box?​

Answer 1

Soln:

Given,

According to question, In AP,

let the first  four consecutive boxes be: a-d, a, a+ d, a+2d

Sum of first 4 boxes= 24

a-d+a+a+d+a+2d= 24....(i)

difference between any two consecutive boxes = 2

a-(a-d)=2...(ii)

Fifth term($t_{5}$)=?

now,

solving (II),

a-(a-d)=2

or, a-a+ d=2

:. d=2

Again, solving (I),

a-d+a+a+d+a+2d= 24

when d=2,

a-2+a+a+2+a+2×2=24

or, 4a+4=24

or, 4(a+1)=24

or, a+1=6

:. a=5

________________________________________________________

now,

As per given, first term(t1)=a-d

where, a=5, d=2

so, t1= 3

similarly, common difference(d')= t2-t1

                                                    =a-(a-2)

                                                   = a- a+ d

                                                   = d

                                                   =2

__________________________________________________________

At last,

As per rule of AP,

              t n=t1+(n-1)d'

           or,t5=3+(5-1)×2

           :. t5= 11

Answer 2

Answer:

Step-by-step explanation:

Amazing