# How do you find the first five terms given a_1=6 and a_(n+1)=a_n+n+3?

Oct 11, 2016

First five term are $\left\{6 , 10 , 15 , 21 , 28 , \ldots \ldots\right\}$

#### Explanation:

As ${a}_{n + 1} = {a}_{n} + n + 3$

${a}_{2} = {a}_{1} + 1 + 3 = 6 + 1 + 3 = 10$

${a}_{3} = {a}_{2} + 2 + 3 = 10 + 2 + 3 = 15$

${a}_{4} = {a}_{3} + 3 + 3 = 15 + 3 + 3 = 21$

${a}_{5} = {a}_{4} + 4 + 3 = 21 + 4 + 3 = 28$

Hence first five term are $\left\{6 , 10 , 15 , 21 , 28 , \ldots \ldots \ldots . .\right\}$