Question

G.S and an A.P have common first term which is equall to three if the second term of a G.P is equal to the fourth term of the A.P and the third term of the G.P is equal to the tenth term of an A.P, then find A5,G5

Answer 1

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first term -- a

term3 = a + 2d, but term3 = 4a

4a = a+2d

3a = 2d

term6 = a + 5d = 17

or a = 17-5d

sub that into 3a = 2d

3(17-5d) = 2d

51 - 15d = 2d

51 = 17d

d = 3

then 3a = 6

a = 2

terms are: 2, 5, 8, 11, 14, 17 ,

all checks out,

the fourth terms is 4 times the first

and the 6th is 17