The 17th term of an A.P is 13 times the second term. Prove that the twelve term is five times the third term

Answer 1

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

Answer 2

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

Answer 3

"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!

Answer 4

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Answer 5

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