Question

1. The sum of first n terms of an arithmetic sequence is 3n²+4n

Answer 1

Answer:

          a.  a₁=7,     b.  a_n=7n+1,    c.  a₂₀=141

Step-by-step explanation:

a.

 $a_1=S_1=3\cdot1^2+4\cdot1=3+4=7$

b.

   $a_1+a_2=S_2\\\\a_1+a_1+d=3\cdot2^2+4\cdot2\\\\7+7+d=3\cdot4+8\\\\14+d=12+8\\\\d=6\\\\\\a_n=a_1+d(n-1)\\\\a_n=7+6(n-1)\\\\a_n=7+6n-6\\\\\underline{a_n=7n+1}$

c.

 $a_{20}=7\cdot20+1=141$