Answer:
There are 16 blocks in the 7-th row
There are 220 blocks in all
Further explanation
This problem is about Arithmetic Progression.
40 , 36 , 32 , 28 , 24 , ... , 440,36,32,28,24,...,4
where:
a = 40
d = 36 - 40 = -4
Let's find the number of blocks in the 7th row:
{T_n = a + (n-1)d}
=a+(n−1)d
T_7 = 40 + (7-1)(-4)T
7
=40+(7−1)(−4)
T_7 = 40 + 6(-4)T
7
=40+6(−4)
T_7 = 40 - 24T
7
=40−24
T_7 = 16T
7
=16
Let's find the total number of blocks:
{T_n = a + (n-1)d}
T
n
=a+(n−1)d
4 = 40 + ( n - 1 )(-4)4=40+(n−1)(−4)
4 - 40 = ( n - 1 )(-4)4−40=(n−1)(−4)
-36 = ( n - 1 )(-4)−36=(n−1)(−4)
-36 \div -4 = ( n - 1 )−36÷−4=(n−1)
9 = n - 19=n−1
n = 9 + 1n=9+1
n = 10n=10
{S_n = \frac{1}{2}n ( 2a + (n-1)d )}
S
n
=
2
1
n(2a+(n−1)d)
S_{10} = \frac{1}{2}(10) ( 2(40) + (10-1)(-4) )}
S_{10} = \frac{1}{2}(10) ( 80 - 36 )}
S_{10} = \frac{1}{2}(10) ( 44 )}
S_{10} = 220S
10
=220
Step-by-step explanation:
Answer:
There are 16 blocks in the 7th row.
And there are 220 blocks in all.
Step-by-step explanation:
This problem is about getting the nth term of an arithmetic sequence.
Here's the simple step by step solution of the problem.
Formula/equation:
An=a1 + (n-1) (d)
n = is the term that you are looking for. Eto yung number na hinahanap mo, kung pang ilang row ang hinahanap mo.
a1 = ito yung term na pinakauna sa sequence. Example: 40, 36, 32. Sa sequence na yan, yung 40 ang A1 kase sya yung pinakauna.
d= yung d naman ay kung ilan ang numero ng distansya sa term ng sequence. Para makuha ang d, eto ang simple formula.
(a2-a1 =d)
Example: 40, 36, 32
^ ^
a1 a2
Solution: 40-36 = -4
Now let us solve the problem.
Given:
n = 7 (nth term)
a1 = 40 (kase sya yung unang term)
d = -4 (eto yung distance ng numero)
Solution:
An= a1 + (n-1) (d)
A7= 40 + (7-1) (-4)
A7= 40 + (6)(-4)
A7= 40 + (-24)
A7= 16
So 16 is the 7th row of the blocks.
ps: Feel free to use calculator kung sakaling malilito kayo sa positive/negative signs.
