Hi, can you help me with this, step by step explanation so that i can undertand?

Mathematics

2 answers:

antiseptic1488 [7]3 years ago

8 0

Answer:

2835.

Step-by-step explanation:

The first integer divisible by 7 is 14 and the last one is 196 ( as 7*28) = 196).

We have an Arithmetic series here where each term is increased by 7 to get the next one.

The number of terms (n) = (196 - 14)/ 7 + 1 = 26 + 1 = 27.

The formula for the sum of n terms = (n/2)(a + l) where a = first and l = last term.

So the answer is :

(27/2)( 14 + 196)

= 13.5 * 210

= 2835.

Nimfa-mama [501]3 years ago

5 0

Answer:

Given a = 14

d = 7

an = 196

a + ( n - 1 ) d = 169

14 + ( n - 1 ) 7 = 169

( n - 1 ) 7 = 182

n - 1 = 26

n = 26 + 1

n = 27

Sum = n / 2 ( a + an )

27 / 2 ( 14 + 196 )

27 ( 105 )

2835

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Steve hade 17 pencils in his backpack. this represents 5 more than 6/7 the number of pencils that Clyde has in his backpack

LenaWriter [7]

Answer:

Clyde has 14 pencils in his backpack

Step-by-step explanation:

Let x be the number of pencils that Clyde has in his backpack.

We can translate this statement “<u><em>Steve hade 17 pencils in his backpack. this represents 5 more than 6/7 the number of pencils that Clyde has in his backpack</em></u>” mathematically like this :

$17=5+\frac{6}{7} x \\\\ \Longleftrightarrow 17-5=\frac{6}{7} x \\\\ \Longleftrightarrow 12=\frac{6}{7} x \\ \\\Longleftrightarrow x=\frac{12\times 7}{6} =14$