it the nth of a sequence is denoted by the formula n(2n+1)-3n find the sum of d first four terms
2 n^2 + n -3n = 2 n^2 - 2 n = 2 n(n-1)
n = 1 ---> 0
n = 2 ---> 4
n = 3 ---> 12
n = 4 ---> 24
sum = 16+24 = 40
To find the sum of the first four terms of the sequence, we need to substitute the values of n from 1 to 4 into the formula and then add the results.
Let's calculate the sum step by step:
Step 1: Substitute n = 1 into the formula:
n(2n+1) - 3n = 1(2*1+1) - 3*1
= 3 - 3
= 0
Step 2: Substitute n = 2 into the formula:
n(2n+1) - 3n = 2(2*2+1) - 3*2
= 2(4+1) - 6
= 10 - 6
= 4
Step 3: Substitute n = 3 into the formula:
n(2n+1) - 3n = 3(2*3+1) - 3*3
= 3(6+1) - 9
= 3(7) - 9
= 21 - 9
= 12
Step 4: Substitute n = 4 into the formula:
n(2n+1) - 3n = 4(2*4+1) - 3*4
= 4(8+1) - 12
= 4(9) - 12
= 36 - 12
= 24
The first four terms of the sequence are: 0, 4, 12, 24.
To find the sum, we add these terms together:
0 + 4 + 12 + 24 = 40
Therefore, the sum of the first four terms of the sequence is 40.
To find the sum of the first four terms of a given sequence, we need to substitute the values of n into the formula and then add them together.
The formula for the nth term of the sequence is given as n(2n+1)-3n.
To find the sum of the first four terms, we need to calculate:
1(2(1)+1)-3(1) + 2(2(2)+1)-3(2) + 3(2(3)+1)-3(3) + 4(2(4)+1)-3(4)
Let's calculate each term:
1(2(1)+1)-3(1) = 1(2+1)-3 = 1(3)-3 = 3-3 = 0
2(2(2)+1)-3(2) = 2(4+1)-6 = 2(5)-6 = 10-6 = 4
3(2(3)+1)-3(3) = 3(6+1)-9 = 3(7)-9 = 21-9 = 12
4(2(4)+1)-3(4) = 4(8+1)-12 = 4(9)-12 = 36-12 = 24
Now, let's add all the terms together:
0 + 4 + 12 + 24 = 40
Therefore, the sum of the first four terms of the sequence is 40.