# math sequenc

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the nth term of the geometric progression is 3(2^n-1). how many terms are less than 200?

• math sequenc -

let's see what term is close to 200

3(2^n - 1) = 200
2^n - 1 = 200/3
2^n = 200/3 + 1 = appr 67

I know 2^6 = 64
so n is either 6 or 7

check:
3(2^6 - 1) = 189
3(2^7 - 1) > 200

so there are 6 terms less than 200

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