Complete the following series.
a) 61,110,114,150, ?
b) 14, 25, 49, 169, 256, 169,?
Answers
(a) 61,110,114,150, ..........?
Solve:
1) Taking the first term: 61
Adding both the numbers: 6 + 1 =7
squaring 7: 7*7 = 49
Add: 49+ 61
=> 110................ i.e. the second term
2) Taking the second term: 110
Adding both the numbers: 1 + 1 =2
squaring 2: 2*2 = 4
Add: 110 + 4
=> 114................ i.e. the Third term
3) Taking the third term: 114
Adding the numbers: 1 + 1 + 4 =6
squaring 6: 6*6 = 36
Add: 114 + 36
=> 150................ i.e. the Fourth term
4) Taking the Fourth term: 150
Adding both the numbers: 1 + 5 =6
squaring 6: 6*6 = 36
Add: 150 + 36
=> 186................ i.e. the Final term
Hence, the series is 61,110,114,150, 186
b) 14, 25, 49, 169, 256, 169,?
Solve:
1) Taking the first term: 14
Adding both the numbers: 1 + 4 =5
squaring 5: 5*5 = 25
=> 25................ i.e. the second term
2) Taking the second term: 25
Adding both the numbers: 2 + 5 =7
squaring 7: 7*7 = 49
=> 49................ i.e. the Third term
3) Taking the third term: 49
Adding both the numbers: 4+9 = 13
squaring 13: 13*13 = 169
=> 169................ i.e. the Fourth term
4) Taking the Fourth term: 169
Adding the numbers: 1 + 6 + 9 = 16
squaring 16: 16*16 = 256
=> 256................ i.e. the Fifth term
5) Taking the Fifth term: 256
Adding the numbers: 2 + 5 + 6 = 13
squaring 13: 13*13 = 169
=> 169................ i.e. the sixth term
4) Taking the sixth term: 169
Adding the numbers: 1 + 6 + 9 = 16
squaring 16: 16*16 = 256
=> 256................ i.e. the Final term
Hence, the series is 14, 25, 49, 169, 256, 169, 256
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