×

Hello! Socratic's Terms of Service and Privacy Policy have been updated, which will be automatically effective on October 6, 2018. Please contact hello@socratic.com with any questions.

# What is the nth term of 2,6,11,17,24? Thanks

Mar 8, 2018

#### Answer:

${a}_{n} = \frac{1}{2} \left({n}^{2} + 5 n - 2\right)$

#### Explanation:

We can identify this quadratic sequence by the method of differences:

Write down the given sequence:

$\textcolor{b l u e}{2} , 6 , 11 , 17 , 24$

Write down the sequence of differences between consecutive terms:

$\textcolor{b l u e}{4} , 5 , 6 , 7$

Write down the sequence of differences of those differences:

$\textcolor{b l u e}{1} , 1 , 1$

Having reached a constant sequence, we can match the original sequence with a formula using the initial term of each of these sequences as coefficients:

a_n = color(blue)(2)/(0!)+color(blue)(4)/(1!)(n-1)+color(blue)(1)/(2!)(n-1)(n-2)

$\textcolor{w h i t e}{{a}_{n}} = 2 + 4 n - 4 + \frac{1}{2} {n}^{2} - \frac{3}{2} n + 1$

$\textcolor{w h i t e}{{a}_{n}} = \frac{1}{2} \left({n}^{2} + 5 n - 2\right)$