Question

In the sequence 1 2 2 3 3 3 where n consecutiv eterms have value n the 150th term is

Answer 1

$we \: can \: solve \: this \: as \\ 1 + 2 \times 2 + 3 \times 3 + 4 \times 4........$

$because \: 1 \: is \: once \: and \: 2 \: is \: twice \: and \: 3 \: is \: thrice \: and \: so \: on$

$1 \times 1 + 2 \times 2 + 3 \times 3 + 4 \times 4 + 5 \times 5 + 6 \times 6 + 7 \times 7 = 140 \: \\ and \: if \: we \: add \: 8 \times 8\: this \: with \: 8 \: we \: get \: 204 \\ which \: is \: greter \: then \: 150 \: and \: till \: 7 \times 7 \: it \: be \: 140 \: so \: the \: 150th \: term \: is \: 8$

hope it will help you