Maths-
General
Easy

Question

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

Hint:

## 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:an = a + (n - 1) dApplying this, we get:97 = 13 + (n - 1)(4)4(n - 1) = 97 - 13n - 1 = 84/4n = 22We also have the formula of sum of n term:Sn = n/2 [2a + (n - 1)d]Applying this, we get:S22 = 222/2 [2(13) + (22 - 1)(4)]S22 = 11 [26 + 84]S22 = 11 x 110S22 = 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.