Question

find a,b,c such that the following numbers are in AP:a,7,b,23,c

Answer 1

first term is a
d=second term - first term
=7-a
n=5
last term is c
so,
c=a+(5-1)7-a
c-a=28-4a
c=28-4a+a
c=28-3a eq1
also,
d=c-23
therefore
c=a+(5-1)c-23
c=a+4c-92
a=c-4c+92
a=-3c+92 ×3
3a=-9c+276
3a=28-c
sub.
using elimination method,we get
0=-8c+248
8c=248
c=31
from eq 1
a=28-c/3
a=28-31/3
a=-3/3
a=-1
d=7-a
=7-(-1)
=8
d is also equal to third term - second term
8=b-7
b=8+7
b=15

Answer 2

we know that
a2-a1=a3-a2=a4-a3= a5 -a4
a2-a1=a3-a2
7-a= b-7
a+b =14 ....(1)
a3-a2=a4-a3
b-7=23-b
2b =30
b = 15 ... (2)
put the value of b in equation (1)
a+15=14
a=-1
a4-a3= a5 -a4
23 -b =c-23
b+c =46 ...(3)
put the value of b in equation (3)
15+c =46
c = 46-15
c =31
∴ a =-1 ,b=15 and c =31