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The sum of 0.6,1.7,2.8, ....... to 100 terms is ____.

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Detailed Solution

The sum of 0.6,1.7,2.8, ....... to 100 terms is 5505.
Given A.P series is

0.6, 1.7, 2.8 … … . to 100

terms.
We know that,

S n = n 2 [2 a + (n − 1) d]

. Using the formula,
Where, n = the total number of terms present in the series.
a = The first term in the sequence.
d =the common difference between the terms

S n = The sum of the arithmetic series .

Here, first term, a = 0.6.
The second term,

a 2 = 1.7

.
Therefore, the common difference is,

d = 1.7 − 0.6 d = 1.1

Calculating the sum of the arithmetic progression using the formula,

⇒ S 100 = 1002 [2 × 0.6 + (100 − 1) × 1.1] = 50 × (1.2 + 108.9) = 50 × 110.1 = 5505

Therefore, the sum of the given arithmetic progression 0.6,1.7,2.8, ....... to 100 terms is 5505.

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