Smart Nigerian Students Win N50,000 Weekly
Do you want to study in the US, UK, Malaysia or anywhere overseas? Click here to Start!

The sum of the first 9terms is 72 and the sum of the next 4terms...

The sum of the first 9terms is 72 and the sum of the next 4terms is 71 find the AP?

To get notifications when anyone posts a new answer to this question,
Follow New Answers

Post an Answer

Please don't post or ask to join a "Group" or "Whatsapp Group" as a comment. It will be deleted. To join or start a group, please click here

JAMB 2019 CBT Mobile App - Download Now, It's Free!
JAMB 2019 CBT Software - Download Now, It's Free!

Answers (1)

DEMISOLAN
1 week ago
S(n) = Sum of ' n ' terms of an arithmetic sequence
n = number of terms
a = First term
a[n] = nth term
d = Common difference between terms
S(n) = ½ * n[ (2a + (n − 1)d ]
S(9) = 72 = ½ * 9[ 2a + (9 − 1)d ]
(72 * 2)/9 = 2a + 8d
2a + 8d = 16
a + 4d = 8
4d = 8 − a
d = (8 − a)/4 . . . . . . 1st equation
S(13) = ½ * 13[ 2a + (13 − 1)d ]
S(13) = ½ * 13[ 2a + 12d ]
S(13) = 13(a + 6d)
S(13) = 13a + 78d
S(13) − S(9) = 71
S(13) − 72 = 71
S(13) = 143
S(13) = 13a + 78d
143 = 13a + 78d
11 = a + 6d . . . . . 2nd equation
The first term:
From 1st equation , d = (8 − a)/4
11 = a + 6(8 − a)/4
11 = a + (48 − 6a)/4
11 = a + 12 − 3a/2
3a/2 − a = 12 − 11
(3a − a)/2 = 1
a/2 = 1
[ a = 2 ]
The common difference :
Again from first equation d = (8 − a)/4
d = (8 − 2)/4
d = 6/4
[ d = 3/2 ]
The A.P.
a[n] = a + (n − 1)d
a[n] = 2 + (n − 1)3/2
a[n] = 2 + 3n/2 − 3/2
a[n] = (3n + 4 − 3)/2
a[n] = (3n + 1)/2
Ask Your Own Question

Quick Questions

See More University of Ibadan Questions
 
JAMB 2019 CBT Software Agents - Click Here to Apply
JAMB 2019 CBT Software - Download Now, It's Free!
JAMB 2019 CBT Mobile App - Download Now, It's Free!