Find the value of the expression 1 – 6 + 2 – 7 + 3 – 8 +……�

1.	Find the value of the expression 1 – 6 + 2 – 7 + 3 – 8 +……… to 100 terms (a) –250 (b) –500 (c) –450 (d) –300
Answer» Correct option (a) –250 Explanation: The series (1 – 6 + 2 – 7 + 3 – 8 +… to 100 terms) can be rewritten as: ⇒ (1 + 2 + 3 + … to 50 terms) – (6 + 7 + 8 + … to 50 terms) Both these are AP’s with values of a and d as → a = 1, n = 50 and d = 1 and a = 6, n = 50 and d = 1, respectively. Using the formula for sum of an A.P. we get: → 25(2 + 49) – 25(12 + 49) → 25(51 – 61) = –250 Alternatively, we can do this faster by considering (1 – 6), (2 – 7), and so on as one unit or one term. 1 – 6 = 2 – 7 = … = –5. Thus the above series is equivalent to a series of fi fty –5’s added to each other. So, (1 – 6) + (2 – 7) + (3 – 8) + … 50 terms = –5 x 50 = –250

Find the value of the expression 1 – 6 + 2 – 7 + 3 – 8 +……… to 100 terms (a) –250 (b) –500 (c) –450 (d) –300

Answer»

Correct option (a) –250

Explanation:

The series (1 – 6 + 2 – 7 + 3 – 8 +… to 100 terms) can be rewritten as:

⇒ (1 + 2 + 3 + … to 50 terms) – (6 + 7 + 8 + … to 50 terms)

Both these are AP’s with values of a and d as →

a = 1, n = 50 and d = 1 and a = 6, n = 50 and d = 1, respectively.

Using the formula for sum of an A.P. we get:

→ 25(2 + 49) – 25(12 + 49)

→ 25(51 – 61) = –250

Alternatively, we can do this faster by considering (1 – 6), (2 – 7), and so on as one unit or one term. 1 – 6 = 2 – 7 = … = –5. Thus the above series is equivalent to a series of fi fty –5’s added to each other.

So, (1 – 6) + (2 – 7) + (3 – 8) + … 50 terms = –5 x 50 = –250

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