Answer:
15
Step-by-step explanation:
In the previous answer halfway through they used the equation: 960 = (<em>n</em>÷2)×(2<em>a</em>+(<em>n</em>-1)×(7<em>a</em>÷15))
Using this equation we can substitute an number to replace <em>n</em>, the higher the number is the smaller <em>a </em>would be.
When we substitute 15 into <em>a, </em>then it leaves us with the answer to be <em>a </em>= 15 which is a positive integer and also is smaller than 20, this then let’s us know that 15 is how many terms can be summed up to make 960.
To double check this answer you can find that <em>d</em> = 7 by changing the <em>a</em> into 15 in the formula 7<em>a</em>/15 (found in the previous answer.
Then in the expression: (<em>n</em>÷2)×(2<em>a</em>+(<em>n</em>-1)×d)
substitute:
<em>n </em>= 14 (must be an even number for the equation to work)
<em>a</em> = 15
<em>d</em> = 7
This will give you an answer of 847, but this is only 14 terms as we changed <em>n</em> into 14. To add the final term you need to complete the following equation: 847+(<em>a</em>+(<em>n</em>-1)×<em>d</em>)
substituting:
<em>n </em>= 15
<em>a</em> = 15
d <em>= 7</em>
This will give you the answer of 960, again proving that it takes 15 terms to sum together to make the number 960.
I hope this has helped you.
P.S. Everything in the previous solution was right apart from the start of the last section and the answer