Find the 97th term of the arithmetic sequence

Mathematics

1 answer:

kozerog [31]3 years ago

3 0

<h2>Answer:</h2><h2>The 97th term in the series is 409</h2>

Step-by-step explanation:

The given sequence is 25, 29, 33, ....

The sequence represents arithmetic progression

In an AP, the first term is a1 = 25

The difference between two terms, d = 29 - 25 = 4

To find the 97th term,

By formula, $a_{n} = a_{1} + (n - 1) d$

Substituting the values in the above equation, we get

$a_{97} = 25 + (97 - 1) 4$

= 25 + (96 * 4)

= 25 + 384

= 409

The 97 th term in the given sequence is 409.

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<h3>Answer: Third choice. $\overline{AC} \perp \overline{BD}$ </h3>

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Explanation:

SAS stands for Side Angle Side. Note how the angle is between the two sides. To prove the triangles congruent with SAS, we need to know two sides and an angle between them.

We already see that BC = CD as shown by the tickmarks. Another pair of sides is AC = AC through the reflexive theorem.

The missing info is the angle measures of ACB and ACD. If we knew those angles were the same, then we could use SAS to prove triangle ACB is congruent to triangle ACD.

It turns out that the angles are congruent only when they are 90 degrees each, leading to AC being perpendicular to BD. We write this as $\overline{AC} \perp \overline {BD}$ . The upside down T symbol meaning "perpendicular" or "the two segments form a right angle".