The first
term of an
A.P whose 8th and 12th terms are 39 and 59
respectively
Answers
HEY MATE,
GIVEN :
The 8th term of an AP is 39 .
The 12th term of an AP is 59.
TO FIND :
The AP
ANSWER :
The general term,tn =
where n is the nth term.
a is the first term.
d is the common difference.
t8 = a + ( 8 - 1) d
a + 7d = 39 ________(1)
t12 = a + (12 - 1) d
a + 11d = 59 _________(2)
Subtract (1) & (2) ,
(2) => a + 11d = 59
(1) => a + 7d = 39
_________________
4d = 20
d = 20/4
d = 5 .
Substitute the value of d = 5 in equation (1),,,,
(1) => a + 7 (5) = 39
a + 35 = 39
a = 39 - 35
a = 4
The first term of an AP is 4 .
PLEASE CONSIDER MARKING THIS ANSWER AS BRAINLIEST...
hey
Hope this will help you
8th term = a + 7d = 39 ........... (i)
8th term = a + 7d = 39 ........... (i)12th term = a + 11d = 59 ........... (ii)
8th term = a + 7d = 39 ........... (i)12th term = a + 11d = 59 ........... (ii)(i) - (ii);
8th term = a + 7d = 39 ........... (i)12th term = a + 11d = 59 ........... (ii)(i) - (ii);Or, a + 7d - a - 11d = 39 - 59
8th term = a + 7d = 39 ........... (i)12th term = a + 11d = 59 ........... (ii)(i) - (ii);Or, a + 7d - a - 11d = 39 - 59Or, 4d = 20
8th term = a + 7d = 39 ........... (i)12th term = a + 11d = 59 ........... (ii)(i) - (ii);Or, a + 7d - a - 11d = 39 - 59Or, 4d = 20Or, d = 5
8th term = a + 7d = 39 ........... (i)12th term = a + 11d = 59 ........... (ii)(i) - (ii);Or, a + 7d - a - 11d = 39 - 59Or, 4d = 20Or, d = 5Hence, a + 7 × 5 = 39
8th term = a + 7d = 39 ........... (i)12th term = a + 11d = 59 ........... (ii)(i) - (ii);Or, a + 7d - a - 11d = 39 - 59Or, 4d = 20Or, d = 5Hence, a + 7 × 5 = 39Thus, a = 39 - 35 = 4