Question

Find next term of the series $ 7,28,49,70,91,112,... $
A. $ 135 $
B. $ 134 $
C. $ 133 $
D. $ 130 $

Answer 1

Hint: First of all find the correct pattern of the sequence and then find the next succeeding number for the given sequence. Try finding the common difference or common ratio between the two successive numbers to identify the type of sequence.

Complete step-by-step answer:
Given series: $ 7,28,49,70,91,112 $
Here the difference between the terms is –
 $
  28 - 7 = 21 \\
  49 - 28 = 21 \\
  70 - 49 = 21 \\
  91 - 70 = 21 \\
  112 - 91 = 21 \;
  $
We can observe that there is a common difference of $ 21 $ between the two consecutive terms.
Therefore, next term will be $ 112 + 21 = 133 $ \[\]
From the given multiple choices, the option C is the correct answer.
So, the correct answer is “Option C”.

Note: Be very very careful to find out the correct pattern of the sequence. Always remember that in arithmetic sequence the common difference between the two remains the same while in geometric progression the common ratio remains the same between the terms.