biancaaa012
biancaaa012 biancaaa012
  • 29-04-2022
  • Mathematics
contestada

If an arithmetic sequence has a4 = 107 and a8 = 191, what is a₁?
PLEASE HELP ME​

If an arithmetic sequence has a4 107 and a8 191 what is aPLEASE HELP ME class=

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loneguy
loneguy loneguy
  • 29-04-2022

[tex]\text{nth term of an arithmetic sequence,}\\\\a_n = a_1 + (n-1)d\\\\a_4 = a_1 +3d=107~~~......(i)\\ \\a_8=a_1+7d = 191~~~......(ii)\\\\\\\text{(ii) -(i):}\\\\~~~~~~a_1+7d-a_1-3d = 191 -107\\\\\implies 4d = 84\\\\\implies d = \dfrac{84}4\\\\\implies d= 21\\\\\text{Substitute d= 21 in eq~(i):}\\ \\~~~~~ a_1 +3(21) = 107\\\\\implies a_1 + 63 = 107\\\\\implies a_1 = 107-63\\\\\implies a_1 =44[/tex]

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