Question

Find the sum of 0.6 1.7 2.8 to 100 terms

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Answer 1

Answer:

$\bf \color{red}Question :$

Find the sum of 0.6 1.7 2.8 to 100 terms

$\bf \purple{Solution: }$

$\bf \: Given,$

$\bf \: First \: term, a = 0.6$

$\bf \: Common \: difference, d = a_{2} - a_{1}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \bf= 1.7 -0.6$

$\bf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 1.1$

$\bf \: Number \: of \: terms, n = 100$

Formula for sum of the nth term in the AP series is,

$\boxed{\color{blue}{\sf S _{n}= \frac{n}{2} \:[2a + (n − 1)d]}}$

$\bf \: S _{100} = \frac{100}{2} [2(0.6) + (100 – 1)1.1]$

$\: \: \: \: \: \: \: \: \: \: \: \bf= 50[1.2 + (99) \times (1.1)]$

$\: \: \: \: \: \: \: \: \: \: \: \bf= 50[1.2 + 108.9)$

$\: \: \: \: \: \: \: \: \: \: \: \bf= 50[110.1]$

$\: \: \: \: \: \: \: \: \: \: \: \bf= 5505$

$\bf \color{red}{Sum \: of \: first \: 100 \: terms = 5505}$

Answer 2

Answer:

Refer to the attachment for answer