Question

The 9th term of arithmetic sequence is 37 and 16th term is 65 find the 100th team
.​

Answer 1

a₁₀₀ = 385

Explanation:

The nth term of arithmetic sequence is
`a_n=a_1+d(n-1)`

So:

`a_9=a_1+d(9-1)\\\\37=a_1+8d\\\\a_1=37-8d\\\\\\a_(16)=a_1+d(16-1)\\\\65=a_1+15d\\\\65=37-8d+15d\\\\28=7d\\\\d=4\\\\a_1=37-8\cdot4=5\\\\\\a_(100)=a_1+d(100-1)=5+4\cdot95=385`