Question

an arithmetic sequence has a1=5 and a5=13. how many terms of this sequence must be added to get to 60

Answer 1

@Awolflover1

Answer 2

Use the arithmetic sequence formula to first find the common difference.

Answer 3

whats the formula

Answer 4

\[\Large a_n = a_1 +(n-1)d\]you have a1 already. So plug in a5 to find d.\[\Large a_5 = a_1 +(5-1)d\]

Answer 5

so 2

Answer 6

\[\Large 13 = 5 +(5-1)d\]Do you mean d=2? if so, say so...

Answer 7

Now use the sum formula.\[\Large S_n =\frac{ n }{ 2 }[2a_1 + (n-1) d]\]you're told the sum is 60 and you need n (and you know a1 and d from earlier):
\[\Large 60=\frac{ n }{ 2 }[2(5) + (n-1)*2]\]

Answer 8

You could also do it this way... write out the terms and see how many you need to add to get 60

5, 7, 9, 11, 13,... etc