Question

The same of first 6 terms of an AP is 42 the ratio of its 11th term to its 30th term is 1:3 calculate the first term of an ap

Answer 1

S6=42 a11:a30=1:3
n/2(2a+(n-1)d)=42 (a+10d)/(a+29d)=1/3
6/2(2a+(6-1)d)=42 3a+30d=a+29d
3(2a+5d)=42 3a-a+30d-29d=0
2a+5d=42/3 2a+d=0
2a+5d=14 d=-2a (1)
2a+5(-2a)=14 (from (1))
2a-10a=14
-8a=14
a=14/-8
a= -7/4
Put in(1)
d= -2(-7/4)
d=7/2