Question

the sum of 6 terms of an AP is 42. The ratio of its 10th term to 30th term is 1:3.Find the first and the 13th term of the AP

Answer 1

s6=6/2(2a+5d)=42
=12a+5d=14
=2a+5d=14 -------(1) {dividing by 6}
now,
a10/a30=1/3
a+9d/a+29d=1/3
3a+27d=a+29d
3a-a+27d-29d=0-------(2)
from (1) and (2)
2a+5d=14
2a-2d=0
- + -
__________
7d=14
d=7
put the value of d=7 in eq (1)
2a-2*2=0
2a-4=0
2a=4
therefore,
a13=a+12d
=2+12*2
=2+24
26
hence,1st term=2
13th term=26

Answer 2

Answer is in Attachment

Hope it Helps