Question

In an AP , if the sum of 4th and 8th term is 70 and its 15th term is 80.Find the sum of first 25 terms

Answer 1

is common diff. given

Answer 2

so what is it we know: spose we start at a4, or some other term and call it a1 then:

a1 + a5 = 70
a12 = 80

but not sure if this thought is good yet

Answer 3

not alot to go on :/

Answer 4

it would help if we knew what kind of sequence it was, geometric, artithmetic, other

Answer 5

its given it is a arithmetic progression

Answer 6

ahh, AP. I thought that meant it was an AP class lol

Answer 7

1, 69 in 5 terms would give us

a5 = a1 + d(5-1)

69 = 1 + 4d

68/4 = d = 17

1, 18, 35, 52, 69 is a way to find any d

how far off the mark are we?

a12 = 1 + 17(11)

80 = 1 + 181 ..... a bit ff, but it narrows it down

Answer 8

dude i think we first need to find comm. diff

Answer 9

may 30 and 40?

40 = 30 + 4d

10/4 = d = 5/2

80 = 30 + (5/2)11

80 = 30 + 55/2

80 = 57 is close :)

Answer 10

don't use trial and error method.....

Answer 11

finding a common diff is the way to go, but trial and error is a good way to narrow down the options

Answer 12

its not good

Answer 13

im not saying its the best option; but its not an unusable option

Answer 14

ya but then we should do sumthin else

Answer 15

(Think)(Think)(Think)(Think)(Think)(Think)

Answer 16

exactly; get a feel for it, then let your mind expand upon it ;)

Answer 17

see a4=a+3d,a5=a+4d
so a4+a5=2a+7d
2a+7d=70
now what?

Answer 18

you know at least one term, sub it in for value someplace

Answer 19

and since 15th term =80,
a+14d=80

Answer 20

a4 + a5 is a bit off; try a4 + a8 = 70 maybe?

Answer 21

a=20,d=30/7

Answer 22

we can now find all nos and add them

Answer 23

a4 = a1 + 3d
a8 = a1 + 7d
------------
70 = 2a1 + 10d

Answer 24

a+3d+a+7d=70
2a+10d=70
2(a+5d)=70
a+5d=35-------1

a+14d=80------2

subtract 1 from 2

a+14d=80
-a-5d=-35
-----------
9d=45
d=5

substituting d in 1

a+5(5)=35
a+25=35
a=10

Sn=(n/2)*[2a+(n-1)d]
S25=(25/2)*[(2*10)+(24)5]
=(25/2)*[20+120]
=(25/2)*(140)
=1750

Answer 25

from 1 and 2 we can cramer it to get a and d as well:

d = 80-35 / 14-5
= 45/9
= 5

a = 80(5)-14(35) /-9
= -90 /-9
= 10