Question

p= 2^2+6^2+10^^2+........94^2 and q = 1^2+ 5^2 +9^2 +.......81^2 then find p-q​

Answer 1

Answer:

33

Step-by-step explanation:

p=4+36+100 = 140

q=1+25+81=107

p-q = 140-107 = 33

Answer 2

(p - q) = 26075

Step-by-step explanation:

Given that p = 2² + 6² + 10² + .................. + 82² + 86² + 90² + 94²

and, q = 1² + 5² + 9² + ................ + 81²

Therefore,

(p - q) = (2² - 1²) + (6² - 5²) + (10² - 9²) + ....... + (82² - 81²) + (86² + 90² + 94²)

⇒ (p - q) = (2 + 1) + (6 + 5) + (10 + 9) + ....... + (82 + 81) + (24332)

{Since, (a² - b²) = (a + b)(a - b) and here (a - b) is one or all the cases}

⇒ (p - q) = 3 + 11 + 19 + ......... + 163 + (24332)

The sum (3 + 11 + 19 + ........ + 163) is an A.P. sum with first term 3, common difference 8 and the number of terms is 21.

⇒ (p - q) = $\frac{21}{2}[2 \times 3 + (21 - 1) \times 8] + 24332$

⇒ (p - q) = 1743 + 24332 = 26075 (Answer)