Question

In an AP, an = 28 , S = 144 , n = 9, find 'a' the first term and 'd' the common difference.

Answer 1

Hence value of a=4,d=3.

Answer 2

here an = 28
sn = 144
n = 9
a =?
d = ?
an = a+(n-1) d
28 = a + (9-1)d
28 = a + 8d. ----- ( equation 1 )

sn = n/2 (2a + (n-1) d)
144 = 9/2 ( 2a + (9-1)d)
144(2) = 9( 2a + 8d )
288 = 18a +72d
18( 16 = a + 4d )
16 = a + 4d -------- ( equation 2)

by doing elimination method we can find the value of a and d

a+8d = 28
a+4d = 16
- - -
_________
4d = 12
d = 12/4
d = 3
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by putting the value of d in eq ( 2)
a + 4 ( 3) = 16
a = 16 - 12
a = 4
___________________________
therefore a = 4 and d = 3