Question

What is the nth term for quadratic sequence 7,14,23,34,47,62,79

Answer 1

Answer:

The n-th term for the sequence will be:  $n^2+4n+2$

Step-by-step explanation:

Given sequence is:  7, 14, 23, 34, 47. 62, 79, ........

The n-th term of a quadratic sequence is:  $t_{n}=an^2 +bn+c$

For $n=1$....

$t_{1}=a(1)^2+b(1)+c\\ \\ a+b+c=7 .............................(1)$

For $n=2$....

$t_{2}=a(2)^2+b(2)+c\\ \\ 4a+2b+c=14 .............................(2)$

For $n=3$....

$t_{3}=a(3)^2+b(3)+c\\ \\ 9a+3b+c=23 .............................(3)$

Subtracting equation (1) from equation (2), we will get......

$3a+b=7..........................(4)$

Subtracting equation (2) from equation (3), we will get.......

$5a+b=9..........................(5)$

Now, subtracting equation (4) from equation (5)...........

$2a=2\\ \\ a=\frac{2}{2}=1$

Plugging this  $a=1$ into equation (4), we will get....

$3(1)+b=7\\ \\ 3+b=7\\ \\ b=7-3=4$

Now, plugging $a=1$ and $b=4$ into equation (1) .........

$1+4+c=7\\ \\ 5+c=7\\ \\ c=7-5=2$

Thus, the n-th term for the sequence will be:  $n^2+4n+2$