After inserting n AM between 2 and 38 the sum of the resulting progression is 200 the value of n is
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Answer:
value of n is 8
Step-by-step explanation:
After inserting n AM between 2 and 38, the total number of terms = n+2
common difference = d = (38-2)/(n+1) = 36/(n+1)
sum of the resulting progression is 200
=> (n+2)/2 × {2×2+(n+2-1)×36/(n+1)} = 200
=> (n+2){4+(n+1)×36/(n+1)} = 200×2
=> (n+2){4+36} = 400
=> (n+2) × 40 = 400
=> (n+2) = 400/40 = 10
=> n = 10-2 = 8
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