Question

this is an series related sum


Find the sum of the following
(ii) 102,97,92,... up to 27 terms.
​

Answer 1

$\huge\mathcal {Solution}$

Given :

AP = 102 , 97 , 92 , ....upto 27 terms .

To find :

Sn = ?

Solution :

we have ,

d = 97 - 102

d = -5

and a = 102

As we know that ....

$sn \: = \frac{n}{2} (2a + (n - 1)d)$

$sn \: = \frac{27}{2} (2 \times 102 + (27 - 1) - 5)$

$sn \: = \frac{27}{2} (204 + (26 \times - 5)$

$sn = \frac{27}{2} (204 - 130)$

$sn \: = \frac{27}{2}(74)$

$sn \: = \frac{27}{2} \times 74$

$sn \: = 27 \times 37$

$sn \: = 999$

$\huge \mathcal { EXTRA \: INFORMATION }$

Sum of series = The sum of the given sequence is called as the sum of series .

The formula used in the solution is ..

$sn \: = \frac{n}{2} (2a + (n - 1)d)$

Answer 2

$\huge \mathfrak{answer = > }$

Given -

102,97,92,... up to 27 terms.

a = 102

d = a² - a¹

d = 97 - 102

d = - 5

We know That,

• sn = n/2 {2a + (n-1)d}

Now, according to given information

• sn = 27/2 {2 × 102 + (27-1)-5}

• sn = 27/2 (204 + 26 × -5)

• sn = 27/2 (204 - 130)

• sn = 27/2 × 74

• sn = 27 × 37

• sn = 999

• Hence,

sum of the following terms is -

• sn = 999