Consider the following sequence:
- Find the sum of 2 + 6 + 10 + 14 + ... + 90.
- A given line of the sequence is as follows: 2 + 6 + 10 + 14 + ... + c = 392 = 2 x d2. Find the value of d.
- Calculate the sum of Line 17 if the pattern for the sum of the lines is as follows:-
Line 1: 8
Line 2: 8 + 10
Line 3: 8 + 10 + 12
(a)
Sum of 1 number:
2 =
2 x
12Sum of 2 numbers:
2 + 6 = 8 =
2 x
22Sum of 3 numbers:
2 + 6 + 10 = 18 =
2 x
32 Sum of 4 numbers:
2 + 6 + 10 + 14 = 32 =
2 x
42
Formula:
Sum of numbers =
2 x
Number of numbers in the string2
To find out how many numbers are in the string if 90 is the last number.
Last number in sum of 1 number:
2 = 1 x 4 - 2
Last number in sum of 2 numbers:
6 = 2 x 4 - 2
Last number in sum of 3 numbers:
10 = 3 x 4 - 2
Last number in sum of 4 numbers:
14 = 4 x 4 - 2
Formula:
Last number =
Number of numbers in the string x 4 - 290 = Number of numbers x 4 - 2
90 + 2 = Number of numbers x 4
92 = Number of numbers x 4
Number of numbers
= 92 ÷ 4
= 23
Sum of 23 numbers
= 2 x Number of numbers in the string
2
= 2 x 23
2= 2 x 23 x 23
= 2 x 529
= 1058
(b)
2 x d
2 = 392
d
2 = 392 ÷ 2
d
2 = 196
d = √196
d = 14
(c)
Pattern for the sum of the lines
Line
1: 8 =
2 x (
1 + 1)
2 Line
2: 8 + 10 = 18 =
2 x (
2 + 1)
2 Line
3: 8 + 10 + 12 = 32 =
2 x (
3 + 1)
2 Formula:
Sum of Line Number =
2 x (
Line Number + 1)
2Sum of Line
17 =
2 x (
17 + 1)
2 = 2 x 18
2 = 2 x 18 x 18
= 648
Answer(s): (a) 1058; (b) 14; (c) 648