Question 1088223: The sum of the first q term of an A.p. 162.the ratio of 6th term and it's 13 the term is 1:2.find the 1st and 15th term.of A.P. this mathematics why q assuming 9.please answer
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! Arithmetic progression'
an=a1+d(n-1)
a6=a1+5d
a13=a1+12d
2(a1+5d)=a1+12d
a1=2d
if sum of first 9 terms is 162 (not clear here)
162=(9/2)(a1+a9)
324=9(a1+a9)
36=a1+a9
a9=a1+8d
36-a1=a1+8d
but a1=2d
36-2d=2d+8d
12d=36
d=3
a1=6
the sequence is 6,9,12,15,18,21,24,27,30,33,36,39,42,45,48
21/42 is ratio of 6 and 13 terms
first term is 6, and 15th term is 48
sum of first 9 terms is 162.
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