4. If t2 = -2 and t5 = -8, find t8 and S6.

Question

Two terms of an arithmetic progression are given. Find the indicated term and the indicated sum.

Answer 1

4) Arithmetic series is typically: a, a+d, a+2d, ..., a+(n-1)d, ... where n indicates T_n and d is the common difference, a is the first term.

Therefore, T₂=a+d=-2 and T₅=a+4d=-8. T₅-T₂=3d=-6, d=-2, a=0.

Series is 0, -2, -4, -6, -8, -10, -12, -14, ... so T₈=-14.

Using the formula a+(n-1)d we also get 0+7(-2)=-14 for T₈.

S₆=0-2-4-6-8-10=-30.

We can also use the formula -2n(n+1)/2=-n(n-1)=(-6)(5)=-30 for S₆.