Asked by simranpreet

the sum of first 8 terms of an arithmetic progression is 156.the ratio of its 12th term to its 68th term is 1:5.calculate the first term and the fifteenth term.
please help this questions please.
Answered by Reiny
sum of 8 terms is 156
(8/2)(2a + 7d) = 156
4(2a + 7d) = 156
2a + 7d = 39


(a+11d) : (a + 67d) = 1 : 5

(a+11d)/(a+67d) = 1/5
5a + 55d = a + 67d
4a = 12d
a = 3d

sub that into 2a+7d=39
6d + 7d = 39
13d=39
<b>d=3 , then in a = 3d ---> a = 9</b>

first term is 9
term 15 = a+14d = 9+14(3) = 51

check:
sum(8) = (8/2)(18 + 7(3)) = 4(39) = 156 , checks !
term12 = a+11d = 42
term 68 = a+67d = 210
and 42/210 = 1/5 , YEahh!
Answered by Sujal
Better explain
Answered by Vinah
I haven't get your response yet please help me
Answered by Nanmwa
How many terms has the A.P Whose first term is 15 and the last is 57 given that the common difference is 3
Answered by Precious
Maths
There are no AI answers yet. The ability to request AI answers is coming soon!