Answer:
5) The common difference is [tex]\frac{13}{4} = 3.25[/tex]
6)a) [tex]a(n) = (-138) + (n-1)(200)[/tex]
b) [tex]a(n) = (-1.6) + (n-1)(2.7)[/tex]
Step-by-step explanation:
5) It is given that 10th term is 17 and 14th term is 30.
for any general arithmetic series, the nth term is given by
[tex]a(n) = (a) + (n-1)(d)[/tex] , a= first term and d= common difference.
Inserting both the conditions above, we get
[tex]a(10) = (a) + (9)(d)= 17[/tex]
[tex]a(14) = (a) + (13)(d)= 30[/tex],
solving the above equations we get,
[tex]4(d) = 13[/tex]
[tex]d = \frac{13}{4} = 3.25[/tex] (common difference)
6) a) a(18) =3362 and a(38) = 7362
a(18) = a + (17)(d) = 3362 and a(38) = a + (37)(d) = 7362
Solving the above equation we get, a= -138 and d= 200.
b) a(18) = 44.3 and a(33) = 84.8
a(18) = a + (17)(d) = 44.3 and a(33) = a + (32)(d) = 84.8
Solving the above equation we get, a= -1.6 and d= 2.7
