Question
Download Solution PDFWhich of the following statement is correct?
I. The value of 1002 - 992 + 982 - 972 + 962 - 952 + 942 - 932 + ...... + 222 - 212 is 4840.
II. The value of
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
I. The value of 1002 - 992 + 982 - 972 + 962 - 952 + 942 - 932 + ...... + 222 - 212 is 4840.
II. The value of
Concept used:
A, (A + D), (A + 2D), ....., L is an arithmetic progression with the first term A and common difference D. (L being the Nth term)
Number of terms, N = (L - A)/D + 1
Sum of all terms = (A + L)/2 × N
Calculation:
II. According to the concept,
1002 - 992 + 982 - 972 + 962 - 952 + 942 - 932 + ...... + 222 - 212
(100 + 99)(100 - 99) + (98 + 97)(98 - 97)+...........(22 + 21)(22 - 21)
So, the series will be
100 + 99 + 98 + 97 .............................................22 + 21.
The first term is 100 and the last is 21, the difference is 1.
Sum = (100 + 21) × 80/2 = 121 × 40 = 4840
II.
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∴ Only I is true.
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