Question 33627This question is from textbook Algebra 2
: Please help me explan the steps to any of theae problems or all as you may, it will be very helpful.I have a quiz on it on monday. Thanks for all your Help,I appreciate it with all my Heart.Thanks
Find the indicated term given two other terms
5th term:t4=7 and t7=22
For each arithmetic series,Find S-25
7+13+19+25.....
Based on the terms given,state whether or not each sequence is arithmetic, If it is, identify the common difference,d.
15,18,21,24
This question is from textbook Algebra 2
Answer by sarah_adam(201)   (Show Source):
You can put this solution on YOUR website! 1)given t4 and t7 we need to find out of t5
an arithmetic progression is a sequence starting at a and going up in steps of d
a, a+d, a+2d,..., a+(n-1)d ...
here we know
t4 = a+(4-1)d = a+3d ---- eq 1
t7 = a+(7-1)d = a +6d --- eq 2
but given t4 = 7 and t7 = 22
so a+3d = 7 and a+6d = 22
solving for a and d
(a+6d)-(a+3d) = 22 - 7 (subtracting both equations)
6d - 3d = 22 - 7 = 15
3d = 15
d = 5; a = 7 - 3(5) = 7 - 15 = - 8
a = - 8 and d = 5
now to find t5
t5 = a+(n-1)d
t5 = -8 + (5-1)*5
t5 = -8 +20 = 12
therfore t5 = 12
2)For each arithmetic series,Find S-25
7+13+19+25.....
Sum of n terms in an A.P is Sn = n/2*{2*a+(n-1)*d}
here a = 7 ;d = 13-7 = 6
S25 = (25/2)*{2*7+(25-1)*6}
S25 = (25/2 )*{14+144}
S25 = (25/2) * 148
S25 = 25*74 = 1850
3)Based on the terms given,state whether or not each sequence is arithmetic, If it is, identify the common difference,d.
15,18,21,24
for a series to be in A.P the common difference should be the same
18 - 15 = 3 ( t2 - t1)
21- 18 = 3 ( t3-t2)
24 - 21 = 3 (t4-t3)
so here the c.d is same and hence the series is in A.P and the C.d = 3
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