Question

Find the sum of 0.6 1.7 2.8 to 100 terms

Answer 1

Answer:

Step-by-step explanation:

Given,

0.6 , 1.7 , 2.8 , ..

To Find :-

Sum of first 100 terms

Solution :-

We can say that "0.6 , 1.7 , 2.8 , .." are in A.P

Because :- The common difference(d) is same

1.7 - 0.6 = 2.8 - 1.7

1.1 = 1.1

Common difference(d) = 1.1

First term(a) = 0.6

As we need find sum of 100 terms n = 100

Formula Required :-

$\sf S_n=\dfrac{n}{2}[2a+(n-1)d]$

Let's do :-

$\sf S_{100}=\dfrac{100}{2}[2(0.6)+(100-1)1.1]$

$\sf=50[1.2+99(1.1)]$

$\sf=50[1.2+108.9]$

$\sf = 50(110.1)$

= 5505

Sum of first 100 terms = 5505

Answer 2

$\bf \color{red}Question :$

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,

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

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

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

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

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

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

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