How do you find the next three terms of the arithmetic sequence 19, 24, 29, 34,...?

Mar 17, 2018

Next three terms are color(brown)(39, 44, 49

Explanation:

${a}_{1} = 19$

${a}_{2} - {a}_{1} = d = 24 - 19 = 5$

${a}_{3} - {a}_{2} = d = 29 - 24 = 5$

${a}_{4} - a - 3 = d = 34 - 29 = 5$

Hence ${a}_{1} = 19 , d = 5$

${a}_{5} = {a}_{4} + d = 34 + 5 = 39$

${a}_{6} = {a}_{5} + d = 39 + 5 = 44$

${a}_{7} = {a}_{6} + d = 44 + 5 = 49$

To find the $n \left(t h\right)$ term, ${a}_{n} = {a}_{1} + \left(n - 1\right) \cdot d$