7. The sum of the series:5^{2}-43^{2}+44^{2}-42^{2}+43^{2}-41^{2}+42^{

1.	7. The sum of the series:5^{2}-43^{2}+44^{2}-42^{2}+43^{2}-41^{2}+42^{2}-40^{2}+till 15 terms is(a) 1982(c) 27562592(d) 2832
Answer» we can write as 45² - 43² + 44² - 42² + 43² - 41² + 42² - 40² + 41² - 39² + 40² - 38² + 39² - 37² + 38² = (38² + 39² + 40² + 41² + 42² + 43² + 44² + 45² ) - (37² + 38² + 39² + 40² + 41² + 42² + 43²) = 44² + 45² - 37² = 45² + 44² - 37² = 1225 + (44 - 37) × (44 + 37) = 1225 + 7 × 81 = 1225 + 567 = 1792 No option

7. The sum of the series:5^{2}-43^{2}+44^{2}-42^{2}+43^{2}-41^{2}+42^{2}-40^{2}+till 15 terms is(a) 1982(c) 27562592(d) 2832

Answer»

we can write as 45² - 43² + 44² - 42² + 43² - 41² + 42² - 40² + 41² - 39² + 40² - 38² + 39² - 37² + 38²

= (38² + 39² + 40² + 41² + 42² + 43² + 44² + 45² ) - (37² + 38² + 39² + 40² + 41² + 42² + 43²)

= 44² + 45² - 37²

= 45² + 44² - 37²

= 1225 + (44 - 37) × (44 + 37)

= 1225 + 7 × 81

= 1225 + 567

= 1792

No option