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The n^th term of a sequence is given by T(n)=n^2+70 How many terms in the sequence are less than 100?

Question

The n^th term of a sequence is given by
T(n)=n^2+70
How many terms in the sequence are less than 100?

The n^th term of a sequence is given by T(n)=n^2+70 How many terms in the sequence are less than 100?

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CallumMaster · Tutor for 5 years

Answer

<p> 5 </p>

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<p> This question involves the knowledge of arithmetic sequences. We have a given equation for calculating terms in the sequence, which is \(T(n)=n^{2}+70\). Here, \(T(n)\) represents the nth term of the sequence and n is the term number. To find how many terms of this sequence are less than 100, we need to solve an inequality: \(n^{2}+70<100\), on the basis of the values of natural number n. </p>
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