Answer is 73.5
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Work Shown:
a_5 = 19 and d = -1.3 are given values
a_n = a_1 + d(n-1)
a_n = a_1 + (-1.3)(n-1) replace d with -1.3
a_n = a_1 - 1.3(n-1)
a_5 = a_1 - 1.3(5-1) replace n with 5
a_5 = a_1 - 1.3(4)
a_5 = a_1 - 5.2
19 = a_1 - 5.2 replace "a_5" with 19; isolate a_1
19+5.2 = a_1 - 5.2 + 5.2
24.2 = a_1
a_1 = 24.2
The first term is 24.2 and the common difference is -1.3, so the nth term formula is
a_n = a_1 + d(n-1)
a_n = 24.2 + (-1.3)(n-1)
a_n = 24.2 - 1.3(n-1)
a_n = 24.2 - 1.3n - 1.3(-1)
a_n = 24.2 - 1.3n + 1.3
a_n = -1.3n + 25.5
note: if you plugged n = 5 into that formula above, you should get a_5 = 19
Use this formula to find the 35th term
a_n = -1.3n + 25.5
a_35 = -1.3*35 + 25.5
a_35 = -20
Now we can use the nth term summation formula for arithmetic sequences
s_n = (n/2)*(a_1 + a_n)
s_35 = (35/2)*(a_1 + a_35) replace n with 35
s_35 = (35/2)*(24.2 + (-20))
s_35 = 73.5