Question

Find out the missing terms in the given sequence:
7, 1, 42, D, 1302, F

• A. D = 222, F = 7770
• B. D = 210, F = 7770
• C. D = 210, F = 7788
• D. D = 222, F = 7788

Answer 1

The correct option is B D = 210, F = 7770

Analyzing the sequence, we observe:

$\text{1st term}=7=6^0+6=1+6$

$\text{2nd term}=0=6^1-6=6-6$

$\text{3rd term}=42=6^2+6=36+6$

So, for the odd number terms, the rule is: $6^{n-1}+6$

For the even number terms, the rule is: $6^{n-1}-6$

So, we observe:
$\text{4th term}=\text{D}=6^{4-1}-6=6^3-6=216-6=210$

$\text{5th term}=1302=6^{5-1}+6=6^4+6=1296+6=1302$

$\text{6th term}=\text{F}=6^{6-1}-6=6^5-6=7776-6=7770$

So, the missing values are:
$D=210$
$F=7770$