how many terms of ap : 9,17,25.........should be taken to give a sum 636.
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Heya!!!
Here is your answer.
✴✴✴✴✴✴✴✴✴✴✴✴✴✴
☑ The pattern is 9,17,25.........
☑ The sum of the numbers is 636
If we see the pattern we will see,
↪ (8×1)+1 = 9
↪ (8×2)+1 = 16
↪ (8×3)+1 = 25
✒ 8x + 1 ; here 'x' is the serial no. of the last number or total terms
Now,
♦ We know,
the sum of the numbers of any pattern = {(last number + 1st number)÷2} × serial no. of the last number or total terms.
according to the rule,
636 = [ { ( 8x+ 1 ) + 9 } \ 2 ] × x
• 636 = {8x + 10) \2} × x
• 636 = {(8x\2) + (10\ 2)} × x
• 636 = (4x + 5) × x
• 636 = 4x² + 5x
• 636 = 4x² + 5x
• 636 - 636 = 4x² + 5x - 636
• 0 = 4x² + 5x - 636
• 0 = 4x² + 53x - 48x - 636
• 0 = x ( 4x + 53) - 12 ( 4x + 53)
• (4x + 53) (x - 12) = 0
Now,
if , x - 12 = 0
• x = 12
or, 4x + 53 = 0
• 4x = - 53
• x = - 53 \ 4
But we know serial no. or total terms can not be negative.
So, x = 12
▪ The last number will be {(8×12)+1} = 97
If we want to prove we can write,
(9 + 16 + 25 + 33 + 41 + 49 + 57 + 65 + 73 + 81 + + 89 +97) = 636
❇ So, There are 12 terms in total of the pattern : 9,16,25.....should be taken to give a sum of 636.
❇ Hope it will help you, friend. ☺
Here is your answer.
✴✴✴✴✴✴✴✴✴✴✴✴✴✴
☑ The pattern is 9,17,25.........
☑ The sum of the numbers is 636
If we see the pattern we will see,
↪ (8×1)+1 = 9
↪ (8×2)+1 = 16
↪ (8×3)+1 = 25
✒ 8x + 1 ; here 'x' is the serial no. of the last number or total terms
Now,
♦ We know,
the sum of the numbers of any pattern = {(last number + 1st number)÷2} × serial no. of the last number or total terms.
according to the rule,
636 = [ { ( 8x+ 1 ) + 9 } \ 2 ] × x
• 636 = {8x + 10) \2} × x
• 636 = {(8x\2) + (10\ 2)} × x
• 636 = (4x + 5) × x
• 636 = 4x² + 5x
• 636 = 4x² + 5x
• 636 - 636 = 4x² + 5x - 636
• 0 = 4x² + 5x - 636
• 0 = 4x² + 53x - 48x - 636
• 0 = x ( 4x + 53) - 12 ( 4x + 53)
• (4x + 53) (x - 12) = 0
Now,
if , x - 12 = 0
• x = 12
or, 4x + 53 = 0
• 4x = - 53
• x = - 53 \ 4
But we know serial no. or total terms can not be negative.
So, x = 12
▪ The last number will be {(8×12)+1} = 97
If we want to prove we can write,
(9 + 16 + 25 + 33 + 41 + 49 + 57 + 65 + 73 + 81 + + 89 +97) = 636
❇ So, There are 12 terms in total of the pattern : 9,16,25.....should be taken to give a sum of 636.
❇ Hope it will help you, friend. ☺
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