any 3 successive coefficient in the expansion of (1+x)^n where n is a positive integer are 28,56,70 then n is

Let the terms be ⁿC_r , ⁿC_r+1 , ⁿC_r+2

Now, ⁿC_r+1 /ⁿC_r = (n - r) / (r + 1) = 56 / 28 = 2

After cross multiplying

= n = 3r + 2 = 4n = 12r + 8 ---------- (i)

Now,

ⁿC_r+2 /ⁿC_r+1 = 70 / 56

= (n - r - 1) / (r + 2) = 5 / 4

= After cross multiplying,

4n = 9r + 14----------(ii)

Equating (i) and (ii)

9r + 14 = 12r + 8

3r = 6

r = 2

Applying the value of r in (i)

4n = 12 * 2 + 8

4n = 24 + 8 = 32

n = 8

Hence, n = 8

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