1. Find the sum of first 15 terms of the following APs:
(i) 11, 6, 1, – 4, –9 ...
(ii) 7, 12, 17, 22, 27 ..
Answers
AP:- 11, 6, 1, -4, -9...
Here,
a¹= 11, d= -5, n= 15
Now,
S15= n/2{2a+(n-1)d}
= 15/2{ 2*11+(15-1)(-5)}
= 15/2{22-70}
= 15/2*(-48)
= 15*(-24)
= -360
(ii) Given,
AP:- 7, 12, 17, 22, 27...
Here,
a¹= 7, d= 5, n= 15
Now,
S15= n/2{2a+(n-1)d}
= 15/2{2*7+(15-1)5}
= 15/2{14+70}
= 15/2*84
= 15*42
=630
Hope this helps you!
From now ,
lets name first term as a
lets call the common difference as d
the number of terms is n
and the Sum of n terms is S
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Important formula :
S = n / 2 [ 2 a + ( n - 1 ) d ]
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Lets solve the questions :
1 ) 11 , 6 , 1 ........................ for 15 terms
n = 15
a = 11
d = 6 - 11 = - 5
or , = 1 - 6 = -5
S of 15 terms ==> S = n / 2 [ 2 a + ( n - 1 ) d ]
==> S = 15 / 2 [ 2 × 11 + ( 15 - 1 ) ( - 5 ) ]
==> S = 15 / 2 [ 22 + 14×-5 ]
==> S = 15 / 2 [ 22 -70 ]
==> S = 15 / 2 × [ - 48 ]
==> S = 15 × -24
==> S = -360
The sum of 15 terms is -360.
2 ) 7 , 12 , 17 , 22 .................... 15 terms
n = 15
d = 12 - 7 = 5
a = 7
sum of 15 terms ==> S = n / 2 [2 a + ( n - 1 ) d ]
==> S = 15 / 2 × [ 14 + ( 15 - 1 ) × 5 ]
==> S = 15 / 2 × [ 14 + 14×5 ]
==> S = 15 / 2 × [ 14 + 70 ]
==> S = 15 / 2 × 84
==> S = 15 × 42
==> S = 630
The sum of 15 terms is 630
Hope it helps you
Tell me if there's a mistake ^_^
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