Expert answers to "Find the twenty-eighth positive multiple of 4 and..."

High School
Algebra
Pre-Algebra
Factors and multiples

amanf

Answered question

2021-08-06

Find the twenty-eighth positive multiple of 4 and the sum of the first twenty-eight positive multiples of 4.

a_{28} =

S_{28} =

Answer & Explanation

casincal

Skilled2021-08-07Added 82 answers

Step 1
To calculate the twenty-eighth positive multiple of 4 and the sum of the first twenty-eight positive multiples of 4.
Step 2
Formula used for nth term and sum of n-terms of an AP series are given below:

a_{n} = a + (n - 1) d

S_{n} = \frac{n}{2} (2 a + (n - 1) d)

Where,

a =

first term

d =

common difference

n =

number of terms
Step 3
Now,
Multiple of 4 is:
4, 8, 12, 16……

a = 4

d = 8 - 4 = 12 - 8 = 4

n = 28

As the common difference is same. Therefore, the series is in AP.
Step 4
Therefore,

a_{n} = a + (n - 1) d

a_{28} = 4 + (28 - 1) 4

= 112

S_{n} = \frac{n}{2} (2 a + (n - 1) d)

S_{28} = \frac{28}{2} (2 \cdot 4 + (28 - 1) 4)

= 1624

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