The number of dots in 50th figure is 102
What is Arithmetic Progression?
An arithmetic progression (AP) is a sequence where the differences between every two consecutive terms are the same. In this type of progression, there is a possibility to derive a formula for the nth term of the AP. For example, the sequence 2, 6, 10, 14, … is an arithmetic progression (AP) because it follows a pattern where each number is obtained by adding 4 to the previous term. In this sequence, nth term = 4n-2. The terms of the sequence can be obtained by substituting n=1,2,3,... in the nth term. i.e.,
- When n = 1, first term = 4n-2 = 4(1)-2 = 4-2=2
- When n = 2, second term = 4n-2 = 4(2)-2 = 8-2=6
- When n = 3, thirs term = 4n-2 = 4(3)-2 = 12-2=10
As,
figure 1= 4 dots
figure 2= 6 dots
figure 3= 8 dots
So, we will create an AP
4, 6, 8,..
a=4, d= 2
Now,
a50= a+ (50-1) d
= 4 + 49 * 2
= 4+ 98
= 102
Hence, the 50th figure will contain 102 dots.
Learn more about Arithmetic Progression here:
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