Question

four terms are in ap if sum of numbers is50and largest number is four timesthe smaller one then find the terms.​

Answer 1

Answer:

Step-by-step explanation:

Let the first term be a and common difference be d

Largest  term = a+3d (fourth term)

Smallest term = a

given

4a = a+3d     ----------------(1)

Sum of first four terms = 2(a+a+3d)

2(a+a+3d) = 50 ---------------(2)

2(a+4a)=50            (4a = a+3d)

5a=25

a=5

d=5

Terms = 5,10,15,20

Answer 2

Solution :

Let the four terms are in A.P. are;

• a
• a+d
• a+2d
• a+3d

A/q

$\longrightarrow\rm{a+a+d+a+2d+a+3d=50}\\\\\longrightarrow\rm{4a+6d=50}\\\\\longrightarrow\rm{2(2a+3d)=50}\\\\\longrightarrow\rm{2a+3d=\cancel{50/2}}\\\\\longrightarrow\rm{2a+3d=25......................(1)}$

&

$\longrightarrow\rm{ 4(a)=a+3d}\\\\\longrightarrow\rm{4a=a+3d}\\\\\longrightarrow\rm{4a-a=3d}\\\\\longrightarrow\rm{\cancel{3}a=\cancel{3}d}\\\\\longrightarrow\rm{\pink{a=d}}$

Putting the value of a in equation (1),we get;

$\longrightarrow\rm{2(d)+3d=25}\\\\\longrightarrow\rm{2d+3d=25}\\\\\longrightarrow\rm{5d=25}\\\\\longrightarrow\rm{d=\cancel{25/5}}\\\\\longrightarrow\rm{\pink{d=5}}$

And also a = 5 [∴ a = d]

$\boxed{\bf{Arithmetic\:progression\::}}}}$

$\bullet\:\sf{a=\boxed{5}}}\\\\\bullet\:\sf{a+d=5+5=\boxed{10}}}\\\\\bullet\:\sf{a+2d=5+2(5)=5+10=\boxed{15}}}\\\\\bullet\:\sf{a+3d=5+3(5)=5+15=\boxed{20}}}$