Question

Find the 87th term in the series 2, 10, 26, 50, ..... 1986 2682 3741 4120

Answer 1

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Answer 2

Solution:

→The given series is , 2,10, 26, 50, ..... 1986 2682 3741 4120.

First term = 2 = 8 × 0 + 2

Second term = 10 = 8 × (1) + 2

Third term = 26 = 8 × (3) + 2, 3 = 2+1

Fourth term = 50 = 8 × (6) + 2, 6=1+2+3

Fifth term = 8 × (10) + 2 = 8 × 10 + 2 = 82→10= 1+2+3+4

Sixth term = 8 × (15) + 2 = 120 + 2=122  → 15 =1+2+3+4+5

87 th term  = 8 × Sum of natural numbers from 1 to 86 + 2

                  = 8 ×[ 1+2+3+4+.........86] +2

                   = 8 × $\frac{86\times 87}{2}$ + 2→Given by the formula : 1+2+3+4+5+......n = $\frac{n\times (n+1)}{2}$

                   = 8 × 43 × 87 + 2

                   = 29,928+2

                    = 29,930