Question

Please help me with this #7

Answer 1

`\text{Given that,}\\\\\text{First term,}~ a_1 = -8~~~~...(i)\\\\\text{12th term,}~ a_(12) = -52~~~...(ii)\\\\\text{Common difference is d.}\\\\(ii)/(i):\\\\(a_(12))/(a_1) = (-52)/(-8)\\\\\\\implies (a_1 + (12-1)d)/(a_1) = \frac{52}8\\\\\\\implies (-8+11d)/(-8) = \frac{52}8\\ \\\\\implies -8+11d = \frac{52(-8)}8\\\\\\\implies -8+11d = -52\\\\\\\implies 11d = -44\\\\\\ \implies d = (-44)/(11) = -4`

`\\\text{86th term,} ~a_(86) = a+ (86-1)d \\\\~~~~~~~~~~~~~~~~~~~~=-8+85d\\\\~~~~~~~~~~~~~~~~~~~~=-8+85(-4)\\\\~~~~~~~~~~~~~~~~~~~~=-348\\\\\text{Hence, the 86th term is}~ -348`