Write the first 4 terms of the following formula, start with n = 1. an = 5n nbn = 3!bn = 3n bn = 3n^2 +2n - 6 gn = 1 × 2 × ... n c1 = 2.5, cn = cn-1 + 1.5 d1 = -3, dn = -2dn-1 + 1

Given sequences are:-

$1. a_n=5n\\$

at n=1, $a_1=5$

Similarly $a_2=10, a_3=15, a_4=20$

First four terms are $5,10, 15, 20.$

2.$nbn = 3!bn = 3n bn = 3n^2 +2n - 6$

at n=1

First term is $3(1)^2+2(1)-6=-1$

Similarly other terms at $n=2,3,4$ are $10,27,50$

First four terms are $-1,10,27,50$

3.$g_n=1\times2..\times n$

at n=1, $g_1=1$

Similarly at n=2,3,4

$g_2=2,g_3=6,g_4=24$

First four terms are $1,2,6,24$

4.$c_1=2.5, c_n=c_{n-1}+1.5$

at n=2, $c_2=c_1+1.5=2.5+1.5=4$

at n=3, $c_3=c_2+1.5=4+1.5=5.5$

at n=4, $c_4=c_3+1.5=5.5+1.5=7$

First four terms are $2.5,4,5.5,7$

5.$d_1=-3,d_n=-2d_{n-1}+1$

at n=2, $d_2=-2d_1+1=-2(-3)+1=7$

at n=3, $d_3=-2d_2+1=-2(7)+1=-13$

at n=4, $d_4=-2d_3+1=-2(-13)+1=27$

First Four terms are $-3, 7, -13,27$