Question

If each letter of the alphabet is worth two more than its preceding letter, where A is the first number and equals 1, B is the second number and equals 3,… and Z is the twenty-sixth which equals ….. What is the total value of all the letters in the alphabet?

Answer 1

Answer:

The total value of all the letters in the alphabet is 676.

Step-by-step explanation:

The problem is about an arithmetic sequence where the difference is 2, the first term is 1 and we know that the alphabet has 26 letters.

To find the total sum of all values, we have to use the following formula

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

Where $n=26$, $a_{1}=1$ and $d=2$. Replacing values, we have

$S_{26}=\frac{26}{2}(2(1)+(26-1)2) =13(2+50)=13(52)=676$

Therefore, the total value of all the letters in the alphabet is 676.

Answer 2

Answer:

Step-by-step explanation:

each letter of the alphabet is worth two more than its preceding letter,it means that the worth of each letter is increasing in arithmetic progression. We would apply the formula for determining the nth term of an arithmetic progression. I is expressed as

Tn = a + (n - 1)d

Where

n represents the number of terms in the arithmetic sequence.

d represents the common difference of the terms in the arithmetic sequence.

a represents the first term of the arithmetic sequence.

Tn represents the nth term

From the information given,

n = 26 letters

a = 1

d = 3 - 1 = 2(difference between 2 letters)

Therefore,

T26 = 1 + (26 - 1)2

T26 = 51

The formula for determining the sum of n terms of an arithmetic sequence is expressed as

Sn = n/2[2a + (n - 1)d]

Therefore, the sum of the first 26 terms, S26 would be

S26 = 20/2[2 × 1 + (26 - 1)2]

S26 = 13[2 + 50)

S26 = 13 × 52 = 676