Question

find values of a,b,c such that a ,10,b,c,31are in AP​

Answer 1

givena.p=a,10,b,c,31

we know that a.p=a,a+d,a+2d,a+3d,a+4d,............

therefore a=a
a+d=10. .......eq(1)
a+2d= b
a+3d= c
a+4d=31. .........eq(2)

By eq(1) & eq(2)

a+d=10
a=10-d

we know that a+4d=31

sub 'a' in eq(2)
10-d+4d=31
10+3d=31
3d=21
d=21/3
d=7

a+d=10
a+7=10
a=3

a=a=3
b=a+2d=3+2(7)=17
c=a+3d=3+3(7)=24