Question

Find the next term in the following series.
1. 1260, 640, 340, 200, 140, 120, ____.
2. 840, 168, 42, 14, 7, ____.
3. 111, 108, 99, 81, 72, ____.

Answer 1

Hint: This question is from the topic of number series. In this question, we will first solve 1260, 640, 340, 200, 140, 120, ____. After that, we will solve 840, 168, 42, 14, 7, ____. After that, we will solve 111, 108, 99, 81, 72, ____. We will solve these series by understanding the patterns of the series. After that, we will get our answer.

Complete step by step solution:
Let us solve this question.
In this question, we have asked to find the missing terms of the following series
1260, 640, 340, 200, 140, 120, ____
840, 168, 42, 14, 7, ____
111, 108, 99, 81, 72, ____
So, let us first find out the missing term of the first series that is 1260, 640, 340, 200, 140, 120, ____
In this series, we can see that
Relation between first and second terms: \[\dfrac{1260}{2}+10=640\]
Relation between second and third terms: \[\dfrac{640}{2}+20=340\]
Relation between third and fourth terms: \[\dfrac{340}{2}+30=200\]
Relation between fourth and fifth terms: \[\dfrac{200}{2}+40=140\]
Relation between fifth and sixth terms: \[\dfrac{140}{2}+50=120\]
So, we can say that relation between sixth and seventh terms will be: \[\dfrac{120}{2}+60=120\]
Hence, we can say that the missing term of the series 1260, 640, 340, 200, 140, 120, ____ will be 120.
Now, let us find out the missing term in the series 840, 168, 42, 14, 7, ____
Here, we can say that
840 divided by 5 is 168
168 divided by 4 is 42
42 divided by 3 is 14
14 divided by 2 is 7
So, we can say that 7divided by 1 is 7.
Hence, the missing term of the series 840, 168, 42, 14, 7, ____ is 7.
Now, let us find out the missing term of the series 111, 108, 99, 81, 72, ____
Here, we can say that each succeeding term is written as the preceding term subtracted by sum of digits of the preceding term. We can understand this from the following:
111-(1+1+1)=111-3=108
108-(1+0+8)=108-9=99
99-(9+9)=99-18=81
81-(8+1)=81-9=72
Similarly, we can write
72-(7+2)=72-9=63
So, the missing term in the series 117, 108, 99, 81, 72, ____ is 63

Note: We should have a better knowledge in the topic of number series. Remember that whenever we have to find the missing number in the given series, then we have to find out the rule or pattern in the given series. By using that pattern, we will get the missing term in the series.