Answer:
[tex]S_1_2=\frac{12+1}{2}*12[/tex]
78 blocks.
Step-by-step explanation:
We have been given that a child is building a triangular tower. The first (bottom) row of the 12-row tower is made with 12 blocks. Each successive row uses one less block.
We can see that number of blocks in each row forms an arithmetic sequence, where 1st term is 12, common difference is -1 and number of terms equal to 12.
Let us represent this information as an arithmetic sequence.
[tex]a_n=a_1+(n-1)d[/tex]
Upon substituting our given values in above equation we will get,
[tex]a_n=12+(n-1)*(-1)[/tex]
[tex]a_n=12-n+1[/tex]
[tex]a_n=13-n[/tex]
Therefore, formula of our sequence will be [tex]a_n=13-n[/tex].
Let us find Sum of our sequence using [tex]S_n=\frac{a_1+a_n}{2}*n[/tex].
[tex]S_n[/tex]= Sum of n terms.
[tex]a_n[/tex]=Last term of sequence.
[tex]a_1[/tex]=1st term of sequence.
n= number of terms in the sequence.
Let us find value of last term of our sequence, that is 12th term.
[tex]a_1_2=13-12=1[/tex]
Now let us substitute our values in arithmetic series formula.
[tex]S_1_2=\frac{12+1}{2}*12[/tex]
Therefore, equation representing the total number of blocks used in the tower is [tex]S_1_2=\frac{12+1}{2}*12[/tex].
[tex]S_1_2=\frac{13}{2}*12[/tex]
[tex]S_1_2=13*6[/tex]
[tex]S_1_2=78[/tex]
Therefore, the child has used 78 blocks to make the tower.
Answer:
correct answer is A, i just took the test.
s12= 12/E/k=1 <12+ (k-1)(-1)>
