Question

find the greatest term in the expansion of (10+3x)^12 when x=4

Answer 1

The 12th term in the expansion of (10+3x)^12 will be numerically the greatest.

The greatest term in the expansion of (10+3x)^12 is calculated by using the properties of ratios. For the term T to be maximum, T(r+1) > T(r).

 

T(r+1) / T(r) = ((n – r + 1)/r) x (10x/3)

Substituting n = 12 and x = 4,

 

T(r+1) / T(r) = ((13 – r)/r) x (40/3)

 

For finding the greatest term, T(r+1) > T(r).

 

520 – 40r > 3r

520 > 43r

r < 520/43

r < 12.099

 

Taking r to be an integer, we calculate r to be 12.

 

Hence, the 12th term in the expansion of (10+3x)^12 will be numerically the greatest.

Answer 2

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