Question

If 4, x, y, z, 28 are in A.P. then z is:

(a) 19
(b)23
(c) 22
(d) 27​

Answer 1

Difference (d) = 28-z = z-y = y-x = x-4

First term (a) = 4

Fifth term (a5) = 28

a5 = a + (n-1) * d

28 = 4 + 4d

4d = 24

d= 6

d = 28-z

6 = 28-z

z = 28-6

z = 22

(c) 22

Answer 2

Concept:

Arithmetic progression is a series of numbers where difference between each number of the series from the preceding number is equal.

$n$ th term of an AP is $a_n=a+(n-1)d$ where $a$ is the first term of the AP and $d$ is the common difference of the AP.

and the sum $S=\frac{n}{2}[a+l]$, where $n$ is total number of elements in AP and $a,l$ are the first and last terms of AP respectively.

Given:

Given that, the series of numbers $4,x,y,z,28$ are in AP (Arithmetic Progression)

Find:

The value of the element $z$ of the above Arithmetic progression.

Solution:

Let the common difference of given AP be $=d$

Here for given AP,

First term $(a)=4$

Last term $(l)=28$

Number of elements of AP $(n)=5$

here $x,y,z$ are second, third and fourth elements of AP respectively.

$x=4+(2-1)d=4+d$

$y=4+(3-1)d=4+2d$

$z=4+(4-1)d=4+3d$

Now the sum of the series $=4+(4+d)+(4+2d)+(4+3d)+28=16+6d+28=44+6d$

According to formula,

$44+6d=\frac{5}{2}(4+28)$

$\Rightarrow44+6d=\frac{5}{2}\times32$

$\Rightarrow44+6d=5\times16$

$\Rightarrow44+6d=80$

$\Rightarrow6d=80-44$

$\Rightarrow6d=36$

$\Rightarrow d=\frac{36}{6}=6$

So the value of $z=4+3d=4+3\times6=4+18=22$

Hence the value of z is 22.

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