Asked by Esther

The 17th term of an A.P is 13 times the second term. Prove that the twelve term is five times the third term
Answered by oobleck
you want to show that a+11d = 5(a+2d)
5(a+2d) = 5a + 10d
so, a+11d = 5a + 10d
d = 4a

The 17th term is a + 16d = a + 64a = 65a
5(a+2d) = 5(a + 8a) = 5(13a) = 65a
Answered by R_scott
let s equal the 2nd term , and d equal the difference between adjacent terms

the 17th term equals the second term plus 15 differences
... 13 s = s + 15 d ... 12 s = 15 d ... 4 s = 5 d

the 12th term equals the second term plus 10 differences
... s + 10 d = 9 s

the 3rd term equals the 2nd term plus one difference ... s + d
... 5 (s + d) = 5 s + 5 d = 5 s + 4 s = 9 s

12th equals 5 times 3rd
Answered by Reiny
"The 17th term of an A.P is 13 times the second term"
---> a+16d = 13(a+d)
a + 16d = 13a + 13d
12a = 3d
d =4a
Prove that the twelve term is five times the third term
LS = 12 th term = a + 11d = a + 44a = 45a
RS = 5(third term) = 5(a+2d)
= 5a + 10d
= 5a + 40a = 45a = LS
Done!
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