Answer:
37th term of given arithmetic sequence [tex]a_1[/tex] = 2.3; d = -2.3 is -80.5.
Solution:
Given that
Need to determine 37th term, when [tex]a_1[/tex] = 2.3, d = -2.3
Means first term of arithmetic sequence = [tex]a_1[/tex] = 2.3 and common difference d = -2.3
Formula for nth term of arithmetic sequence is
[tex]\mathrm{a}_{\mathrm{n}}=\mathrm{a}_{1}+(\mathrm{n}-1) \mathrm{d}[/tex] --- equation 1
[tex]\text { In our case } a_{1}=2.3, d=-2.3[/tex]
We need to determine 37th term so n = 37.
On substituting given values in equation (1) we get
[tex]\mathrm{a}_{37}=\mathrm{a}_{1}+(37-1) \mathrm{d}[/tex]
[tex]\begin{array}{l}{\Rightarrow a_{37}=2.3+(37-1)(-2.3)} \\\\ {\Rightarrow a_{37}=2.3(1-36)=2.3 \times 35=-80.5}\end{array}[/tex]
Hence 37th term of given arithmetic sequence is -80.5
