What is the 30th number in the series 1, 2, 4, 7, 11, 16…?

Solution:

1+1=2

2+2=4

4+3=7

7+4=11

11+5=16

16+6=22

22+7=29

29+8=37

37+9=46

46+10=56

56+11=67

67+12=79

79+13=92

92+14=106

106+15=121

121+16=137

137+17=154

154+18=172

172+19=191

191+20=211

211+21=232

232+22=254

254+23=277

277+24=301

301+25=326

326+26=352

352+27=379

379+28=407

407+29=436(30^th Number)

By Formula:

A_n=1+{n(n-1)/2}

Here n=30

A₃₀=1+{30(30-1)/2}

=1+15*29

=1+435

=436