SOLUTION: 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

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

RELATED QUESTIONS
Please help me on this beauty of an equation. I need to complete the ordered pairs so... (answered by stanbon)

hello may u please help me out i don't know all the steps/rules a scatter plot should... (answered by stanbon)

Hi all, im still struggling to do these graph problems, could someone please show me how... (answered by Alan3354)

All right. I had this major hard quiz in algebra, and I'm curious about this one... (answered by Nate)

Hi very helpful tutors, I have one more multiple type word problem on which the second... (answered by math_helper)

Hi, I am doing a question in a assignment where I have to transform the equation to... (answered by ewatrrr)

Respected Sir / Mam , Please help me to solve this question. I will be very grateful for (answered by Edwin McCravy)

Hi, I am working through my Application of derivatives assignment and I have found a lot... (answered by josgarithmetic)

I need help with two more problems. They do not come from a book. I know the answers but... (answered by scott8148)