10. The fifth term of an arithmetic sequence is 11 and the tenth term is 41. What is the first term?
2 answers:
Answer:
-13
Step-by-step explanation:
"Arithmetic sequence" is a big clue, because it means you add on the same amount every time the term number goes up by 1, then add on the same amount to the numbers in the sequence (the list of numbers) see image There are of course formulas to find these missing numbers, but also, crunch it out sometimes so that it makes sense. And when the numbers in the question get crazy you can fall back on the formulas.
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<span>Let's analyze Hannah's work, step-by-step, to see if she made any mistakes.
</span>In Step 1, Hannah wrote
<span> as the sum of two separate derivatives </span>
<span>using the </span><span>sum rule.
</span>
This step is perfectly fine.
In Step 2,
was kept as it is, and 
was rewritten as 
using the constant rule.Indeed, according to the constant rule, the derivative of a constant number is equal to zero.
This step is perfectly fine.
In Step 3,
was rewritten as 
supposedly using the constant multiple rule.
The problem is that according to the constant multiple rule,
should be rewritten as 
and not as 
.
<span>Therefore, Hannah made a mistake in this step.</span>
</span>In Step 1, Hannah wrote
</span>
This step is perfectly fine.
In Step 2,
This step is perfectly fine.
In Step 3,
The problem is that according to the constant multiple rule,
<span>Therefore, Hannah made a mistake in this step.</span>