Question

First term of a sequence is 1 and $\left(n+1\right)$th term is obtained by adding $\left(n+1\right)$ to the $n$th. Find the sequence upto 6th term.

Answer 1

first term $=1$

Consider, $n=1\therefore (n+1{)}^{th}term$, i.e.

$(1+1{)}^{th}$ $2^{nd}term=(1{)}^{th}term+(1+1)$

$=1+2$

$=3.$

For $n=2,3^{rd}term$

$=3+3=6$

For $n=3,4^{th}term$

$=6+(3+1)=10$

Similarly, $5^{th}term=10+5=15$

& $6^{th}term=15+6=21$

& The sequence is $1,3,6,10,15,21$.