Arithmetic
Progressions
9) If the sum of first 7 terms of an AP is 49 and that of 17 terms is 289,
find the sum of first n terms.
Sol:
For given AP:
S7 = 49
& S17 = 289
That means find ‘Sn’
We know that,
Sn =
For given value of S7,
Lets use the formula
Substitute, n = 7
∴ S7 =
∴ 49 =
Take 2 common
∴ 49 =
× 2
(a + 3d)
∴ a + 3d =
7
….(i)
For given value of S17,
Lets use the formula
Sn =
∴ S17 =
∴ 289 =
Take 2 common
∴ 289 =
× 2
(a + 8d)
∴ a + 8d =
17
….(ii)
Equations (i) & (ii) form a pair of linear equations
Lets solve it by elimination method
Subtracting (i) from (ii)
a + 8d =
17
a + 3d =
7
( - )
( - )
( - )
5d =
10
∴ d =
2
∴ a + 6 =
7
Substituting d = 2 in (i)
∴ a + 3(2) =
∴ a =
1
7
Sn =
Substitute,
a = 1 & d = 2
[2(1)
2]
+ (n – 1)
[2
+ 2n – 2]
× 2n
∴ Sn =
n2
Substitute, n = 17
Lets find Sn
Exercise 5.3 9