Answer:
37th term of given arithmetic sequence
= 2.3; d = -2.3 is -80.5.
Solution:
Given that
Need to determine 37th term, when
= 2.3, d = -2.3
Means first term of arithmetic sequence =
= 2.3 and common difference d = -2.3
Formula for nth term of arithmetic sequence is
--- equation 1
![\text { In our case } a_(1)=2.3, d=-2.3](https://img.qammunity.org/2020/formulas/mathematics/high-school/w4atlu7yluqn8uncqhe099mnvohyqggowm.png)
We need to determine 37th term so n = 37.
On substituting given values in equation (1) we get
![\mathrm{a}_(37)=\mathrm{a}_(1)+(37-1) \mathrm{d}](https://img.qammunity.org/2020/formulas/mathematics/high-school/iyxqdw1hq1c6iqzu0nj9fm7rph4udqx1d6.png)
![\begin{array}{l}{\Rightarrow a_(37)=2.3+(37-1)(-2.3)} \\\\ {\Rightarrow a_(37)=2.3(1-36)=2.3 * 35=-80.5}\end{array}](https://img.qammunity.org/2020/formulas/mathematics/high-school/n5xssj4939fgxfephvpnk1ijjjjmfdtxrs.png)
Hence 37th term of given arithmetic sequence is -80.5