Maths-

General

Easy

Question

# The sum of all two digit numbers which when divided by 4 leaves 1 as remainder is

- 1210
- 1200
- 1100
- None

Hint:

### The difference between any two consecutive integers in an arithmetic progression (AP) sequence of numbers is always the same amount. It also goes by the name Arithmetic Sequence. Here we have to find the sum of all two digit numbers which when divided by 4 leaves 1 as remainder.

## The correct answer is: 1210

### A progression of numbers known as an arithmetic sequence is one in which, for every pair of consecutive terms, the second number is derived by adding a predetermined number to the first one.

There are three types of progressions in mathematics. As follows:

- Arithmetic Progression (AP)
- Geometric Progression (GP)
- Harmonic Progression (HP)

In AP, we will come across some main terms, which are denoted as:

- First term (a)
- Common difference (d)
- nth Term (an)
- Sum of the first n terms (Sn)

13,17, 21,...., 97 are two-digit integers that, when divided by 4, leave 1 as the remainder. This creates an A.P. with a common difference of 4 and a first term of 13. Let n represent the A.P's phrase count.

We have the formula of nth term:

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

Applying this, we get:

97 = 13 + (n - 1)(4)

4(n - 1) = 97 - 13

n - 1 = 84/4

n = 22

We also have the formula of sum of n term:

S_{n} = n/2 [2a + (n - 1)d]

Applying this, we get:

S_{22} = 222/2 [2(13) + (22 - 1)(4)]

S22 = 11 [26 + 84]

S22 = 11 x 110

S22 = 1210

Here we used the concept of Arithmetic progression to find the number of terms in the given series. When we study Arithmetic Progression, which is associated with: There are two key formulas we encounter, those were nth term of AP and sum of the first n terms. So therefore the sum is 1210.

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