Arithmetic progression

Level 2

The 3rd term of an arithmetic progression is -9 and the 7th term is -29.Find the 10th term of the progression.

-44 165 44 -165

Ayinde Emmanuel by Ayinde Emmanuel , 21, Nigeria

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1 solution

Noel Lo
May 21, 2015

a 3 = a + 2 d = − 9 a_3 = a+2d = -9 while a 7 = a + 6 d = − 29 a_7 = a+6d = -29 ( a + 6 d ) − ( a + 2 d ) = − 29 − ( − 9 ) (a+6d)-(a+2d) = -29-(-9) so 6 d − 2 d = 4 d = − 20 6d - 2d = 4d = -20 and d = − 5 d=-5 . Now a 10 = a + 9 d = ( a + 6 d ) + 3 d = − 29 + 3 ( − 5 ) = − 29 − 15 = − 44 a_{10} = a+9d = (a+6d) + 3d = -29 + 3(-5) = -29 - 15 = \boxed{-44}

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