Sum of first 18 term of an ap is 100 and the sum of first 19 term is 551.Find the ap
Answers
Here is your answer...
.
.
.
.
.
.
.
.
I HOPE IT MIGHT HELP YOU MORE...
Solution :
A.P or Arithmetic progression
A.P is a sequence in which the next term is obtained by adding a specific number to the previous term .
The specific number that is added is called the common difference of A.P .
Sum of n terms of an A.P is given by the formula :
Sn = n/2 [ 2a + ( n - 1 ) d ]
a = first terms
d = common difference .
Sn = 8/2 [ 2a + ( 8 - 1 )d ]
⇒ 100 = 4 [ 2a + 7d ]
⇒ 2a + 7d = 25 -------------(1)
Similarly for the second case we have :
Sn = 19/2 [ 2a + (19 - 1 )d ]
⇒ 551 = 19/2 [ 2a + 18 d ]
⇒ 29 × 2 = 2 ( a + 9d )
⇒ a + 9d = 29 ------(2)
Multiply (2) with 2 :
2a + 18d = 58 ------(3)
Subtract (1) from (3) :
⇒ 18d - 7d = 58 - 25
⇒ 11 d = 33
⇒ d = 33/11
⇒ d = 3
The common difference is 3 .
2a + 18(3) = 58
⇒ 2a + 54 = 58
⇒ 2a = 4
⇒ a = 4/2
⇒ a = 2
The first term is 2 .
A.P = a , a + d , a + 2d
⇒ 2 , 2 + 3 , 2 + 6
⇒ 2 , 5 , 8