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A pile of blocks has 40 blocks in the bottom row 36 blocks in the second row,32 blocks on the third row and so on until there are only 4blocks on the top row.How many blocks are there in the 7th row?How many blocks are there in all​

Sagot :

Gabrielle43idn

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:

Hope it helps

Mynicknamestakenidn

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.

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