Find the sum of the odd numbers between 11 and 199 inclusive

The sum of the odd number between 11 and 199 inclusive is 9975

The sum of the odd numbers can be calculated below.

The sequence will be as follows

11, 13, 15, 17, 19, 21...…..199

The sequence follows an arithmetic progression. Therefore,

a = first term = 11

common difference = 2

last term = 199

lets find the number of term

a + (n - 1)d = 199

11 + (n - 1)2 = 199

11 + 2n - 2 = 199

2n = 199 - 9

2n = 190

n = 190 / 2

n = 95

Let's find the sum

Sₙ = n /2 (a + l)

S₉₅ = 95 / 2 (11 + 199)

S₉₅ = 47.5 (210 )

S₉₅ = 9975

The sum of the odd number between 11 and 199 inclusive is 9975

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The sum of the odd numbers between 11 and 199 inclusive

= 9,975

Step-by-step explanation:

Old numbers between 11 and 199 are:

111315171921     23252729= 200

313335373941     43454749= 400

515355575961     63656769= 600

717375777981     83858789= 800

9193959799101   103105107109= 1,000

111113115117119121   123125127129= 1,200

131133135137139141    143145147149= 1,400

151153155157159161    163165167169= 1,600

171173175177179181    183185187189= 1,800

191193195197199  = 975

Total sum = 9,975

Classify the odd numbers into 10 columns, then add each row.  Start by adding the first row, which equals 200.  Each successive row of the old numbers will equal 200 more than the previous row sum.  At the end, add all the row sums to get the sum of the old numbers from 11 to 199.

answer is 144

step-by-step explanation:

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