Find the sums
a) 51+52+53+............+80
b) 53+54+55+............+82
c) 102+104+106+...........+160
Answers
Question A
- 51 + 52 + 53 + ........ + 80
Answer
a = 51 = first term
d = 1 = common difference
an = 80
n = number of terms
___________________________
Finding ( n )
an = a + ( n - 1 ) × d
80 = 51 + ( n - 1 ) × 1
80 = 51 + n - 1
80 - 51+1 = n
30 = n
Now .( sn ) sum of numbers.
sn = n/2 ( a + an )
sn = 30/2 ( 51 + 80 )
sn = 15 × 131 = 1965
______________________________________
Question. B
53+ 54 + 55 + ........ + 82
Answer
a = 53 = first term
d = 1 = common difference
an = 82
n = number of terms
___________________________
Finding ( n )
an = a + ( n - 1 ) × d
82 = 53 + ( n - 1 ) × 1
82 = 53 + n - 1
82 - 53 +1 = n
30 = n
Now( sn ) sum of numbers.
sn = n/2 ( a + an )
sn = 30/2 ( 53 + 82 )
sn = 15 × 135 = 2025
______________________________________
Question C
102+104+106+...........+160
Answer.
a = 102 = first term
d = 2 = common difference
an = 160
n = number of terms
___________________________
Finding ( n )
an = a + ( n - 1 ) × d
160 = 102 + ( n - 1 ) × 2
160 = 102 + 2n - 2
160 - 102 + 2 = n
60 = n
Now( sn ) sum of number
sn = n/2 ( a + an )
sn = 60/2 ( 102+ 160 )
sn = 30 × 262 = 7860.
____________________________________
( A )sum of number is --- 1965
( B )sum of number is --- 2025
( C )sum of number is ---- 7860