Simple A.P question (1 Viewer)

[sinophile]

The 4th, 6th and 8th terms of an A.P add up to -6. Find the sixth term.

Ive hit a roadblock here, been thinking about this question for AGES.

 

[Trebla]

The 4th, 6th and 8th terms of an A.P add up to -6. Find the sixth term.

Ive hit a roadblock here, been thinking about this question for AGES.

T_n = a + (n - 1)d
T₄ + T₆ + T₈ = (a + 3d) + (a + 5d) + (a + 7d)
= 3a + 15d
.: 3a + 15d = - 6
3(a + 5d) = - 6
but T₆ = a + 5d
.: 3T₆ = - 6
=> T₆ = - 2

 

[bored.of.u]

The 4th, 6th and 8th terms of an A.P add up to -6. Find the sixth term.

Ive hit a roadblock here, been thinking about this question for AGES.

using the basic form Tn (nth term) = a+(n-1)d

T4 (4th term) = a+3d
T6 (6th term) = a+5d
T8 (8th term) = a+7d

.: T4+T6+T8 = (a+3d)+(a+5d)+(a+7d) = 3a+15d = -6 ----> e1 (equation 1)
.: we also know that T6 = a+5d ----> e2 (equation 2)

then we rearrange e1 to the form 3(a+5d) = -6 ----> e3 (equation 3)
then we substitute e2 into e3

.: 3 T6 = -6
.: T6 = -2

so your 6th term is -2

hope this helped you and good luck =D