Andrew M. answered • 04/19/18
Tutor
New to Wyzant
Mathematics - Algebra a Specialty / F.I.T. Grad - B.S. w/Honors
an = an-1 + n2; a1 = 7
n an
----------
1 7
2 7+22 = 11
3 11+32 = 20
4 20+42 = 36
5 36+52 = 61
Bobosharif S.
The explicit formula for the above sequence is
an=n(n+1)(2n+1)/6+6, n=1,2,...
Report
04/19/18
Salman P.
Here is an explicit formula of the sequence 3, 5, 7,...3,5,7,...3, comma, 5, comma, 7, comma, point, point, point
a(n)=3+2(n-1)a(n)=3+2(n−1)a, left parenthesis, n, right parenthesis, equals, 3, plus, 2, left parenthesis, n, minus, 1, right parenthesis
In the formula, nnn is any term number and a(n)a(n)a, left parenthesis, n, right parenthesis is the n^\text{th}n
th
n, start superscript, t, h, end superscript term.
This formula allows us to simply plug in the number of the term we are interested in, and we will get the value of that term.
In order to find the fifth term, for example, we need to plug n=5n=5n, equals, 5 into the explicit formula.
\begin{aligned}a(\greenE 5)&=3+2(\greenE 5-1)\\\\ &=3+2\cdot4\\\\ &=3+8\\\\ &=11\end{aligned}
a(5)
=3+2(5−1)
=3+2⋅4
=3+8
=11
04/19/18