Question

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

a, what is its first term?
b, write the algebraic form of the sequence.
c, find the 20th term.​

Answer 1

a. a₁=7, b. a_n=7n+1, c. a₂₀=141

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`