Question

Five numbers whose sum is 50 are in AP.If the 5th number is 3 times the 2nd number.Find the number ​

Answer 1

Step-by-step explanation:

what is AP ...

if I get to know the meaning...

I will try

Answer 2

Answer:

$\sf{The \ numbers \ are \ 2, \ 6, \ 10, \ 14}$

$\sf{and \ 18 \ respectively.}$

Given:

$\sf{Five \ numbers \ are \ in \ AP,}$

$\sf{\leadsto{Their \ sum \ is \ 50}}$

$\sf{\leadsto{5^{th} \ number \ is \ 3 \ times}}$

$\sf{the \ 2^{nd} \ number.}$

To find:

$\sf{The \ numbers.}$

Solution:

$\sf{Let \ the \ numbers \ in \ an \ AP \ be}$

$\sf{a-2d, \ a-d, \ a, \ a+d \ and \ a+2d}$

$\sf{According \ to \ the \ first \ condition.}$

$\sf{(a-2d)+(a-d)+a+(a+d)+(a+2d)=50}$

$\sf{\therefore{5a=50}}$

$\sf{\therefore{a=\dfrac{50}{5}}}$

$\boxed{\sf{\therefore{a=10}}}$

$\sf{According \ to \ the \ second \ condition.}$

$\sf{a+2d=3(a-d)}$

$\sf{\therefore{a+2d=3a-3d}}$

$\sf{\therefore{2d+3d=3a-a}}$

$\sf{\therefore{5d=2a}}$

$\sf{But, \ a=10}$

$\sf{\therefore{5d=2(10)}}$

$\sf{\therefore{d=\dfrac{20}{5}}}$

$\boxed{\sf{\therefore{d=4}}}$

$\sf{Numbers \ are}$

$\sf{a-2d=10-2(4)=2,}$

$\sf{a-d=10-4=6,}$

$\sf{a=10,}$

$\sf{a+d=10+4=14,}$

$\sf{a+2d=10+2(4)=18.}$

$\sf\purple{\tt{\therefore{The \ numbers \ are \ 2, \ 6, \ 10, \ 14}}}$

$\sf\purple{\tt{and \ 18 \ respectively.}}$