Question

evaluate the expression given by 83-81+87-85+............+395-393+399-397​

Answer 1

Question :- evaluate the expression given by 83-81+87-85+............+395-393+399-397 ?

Solution :-

we can solve with two methods .

• Either we find sum of all positive terms first, than sum of all negative terms by AP formula and than subtract both sum.
• Or, we can easily make pairs of 2 , as difference between each pair is 2 only. Now, we just have to check how many pairs are their .

Making pairs we get,

→ (83-81) + (87-85) +............+ (395-393) + (399-397)

→ 2 + 2 + _____________ + 2 + 2 .

Now, we have to find how many pairs are their .

we will find value of n by AP.

First terms of pairs are = 83, 87, 91, __________ 399 .

Here,

• First term = a = 83 .
• Last term = Tn = 399 .
• Common Difference = 87 - 83 = 4 .

we know that, nth term of an AP is

• Tn = a + (n - 1)d .

Putting values we get,

→ 399 = 83 + (n - 1)4

→ 399 = 83 + 4n - 4

→ 399 = 79 + 4n

→ 399 - 79 = 4n

→ 4n = 320

dividing both sides by 4,

→ n = 80 .

Therefore,

→ (83-81) + (87-85) +............+ (395-393) + (399-397)

→ 2 + 2 + _____________ + 2 + 2 .

→ 80 Times 2 .

→ 80 * 2

→ 160 (Ans.)

Hence, 160 is correct Answer for given expression.

Learn more :-

If the nth term of an AP is (2n+5),the sum of first10 terms is

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