Given the general term of a sequence u_n = 2n(2n+1), find the sum of the second and fourth terms and select…

Question

Given the general term of a sequence u_n = 2n(2n+1), find the sum of the second and fourth terms and select the correct option.

ScanSolve AI Tutor · Accepted Answer

To solve question 62, we are given the general term of a sequence as $u_n = 2n(2n+1)$ . We need to find the sum of the second and fourth terms.

Find the second term ( $u_2$ ).
Substitute $n=2$ into the formula for $u_n$ :
$u_2 = 2(2)(2(2)+1)$ $u_2 = 4(4+1)$ $u_2 = 4(5)$ $u_2 = 20$
Find the fourth term ( $u_4$ ).
Substitute $n=4$ into the formula for $u_n$ :
$u_4 = 2(4)(2(4)+1)$ $u_4 = 8(8+1)$ $u_4 = 8(9)$ $u_4 = 72$
Find the sum of the second and fourth terms.
Sum $= u_2 + u_4$
Sum $= 20 + 72$
Sum $= 92$
Compare the result with the given options.
The calculated sum is 92, which corresponds to option B.

The final answer is $\text{B. } 92$ .

Given the general term of a sequence u_n = 2n(2n+1), find the sum of the second and fourth terms and select the correct option.