# Sum of #n# terms of a certain series is given by #S_n=2n+3n^2#, what is the type of the series and what is its #20^(th)# term?

##### 2 Answers

It is an arithmetic progression with first term as

#### Explanation:

As sum of

Sum of

Further, sum of

Hence

As sum of

As sum of first three terms is

#### Explanation:

#"calculate the first 'few' terms of the sequence"#

#"using "S_n=2n+3n^2#

#S_1=2+3=5rArra_1=5#

#S_2=4+12=16#

#rArra_2=S_2-S_1=16-5=11#

#S_3=6+27=33#

#rArra_3=S_3-S_2=33-16=17#

#S_4=8+48=56#

#rArra_4=S_4-S_3=56-33=23#

#"the first 4 terms are "5,11,17,23#

#"common difference ( d)"#

#d=23-17=17-11=11-5=6#

#rArr" these terms are an arithmetic sequence with "d=6#

#"the sum to n terms of an arithmetic sequence is"#

#•color(white)(x)a_n=a_1+(n-1)d#

#rArra_20=5+(19xx6)=119#

#rArrS_20=(2xx20)+(3xx20^2)=1240#