Question

Complete the given series
7,9,12,48,?,890

Answer 1

Series Pattern Given Series

7 7

7 × 1 + 1 × 2 9

9 × 2 – 2 × 3 12

12 × 3 + 3 × 4 48

48 × 4 – 4 × 5 172 ✓

172 × 5 + 5 × 6 890

Answer 2

7 , 9 , 12 , 48 , 172 , 890

Solution:

Given series is:

7 , 9 , 12 , 48 , ? , 890

We have to find the missing term

Let us analyse the logic used here

$First\ number = 7\\\\\text{Multiply 1 and add product of 1 and 2 }\\\\7 \times 1 + 1 \times 2 = 7 + 2 = 9\\\\\text{Multiply 2 and subtract product of 2 and 3 }\\\\9 \times 2 - 2 \times 3 = 18 - 6 = 12$

$\text{Multiply 3 and add product of 3 and 4}\\\\12 \times 3 + 3 \times 4 = 36 + 12 = 48\\\\\text{Use the same logic }\\\\\text{Multiply 4 and subtract product of 4 and 5 }\\\\48 \times 4 - 4 \times 5 = 192 - 20 = 172\\\\\text{Multiply 5 and add product of 5 and 6}\\\\172 \times 5 + 5 \times 6 = 860 + 30 = 890$

Thus the complete series is:

7 , 9 , 12 , 48 , 172 , 890

Thus the missing term is 172

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