Question

74. The value of 52 + 62 + ... + 102 + 202 is
(a) 755
(b) 760
(c) 765
(d) 770​

Answer 1

$\large{\boxed{\bf{AnswEr}}}$

• Sum of n terms of the A.P is 2032.

Given :-

• An A.P as 52, 62, .......202

To Find :-

• Sum of its n terms

__________________________

$\large{\boxed{\bf{Solution}}}$

Here,

• First term, a = 52

• Common difference, d = 10

• Tn = 202

★ Formula for finding n terms of an A.P is

$Tn = a + (n - 1)d$

$= > 202 = 52 + (n - 1)10$

$= > 202 = 52 + 10n - 10$

$= > 202 = 42 + 10n$

$= > 10n = 202 - 42$

$= > 10n = 160$

$= > n = \frac{160}{10}$

$= > n = 16$

• Now, we'll find sum of its n terms :-

★ Formula for finding sum of n terms of an A.P is

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

$= > Sn = \frac{16}{2} (2.52 + (16 - 1)10)$

$= > Sn = 8(104 + 150)$

$= > Sn = 254 \times 8$

$= > Sn = 2032$

★Hence, the sum of n terms of the A.P is 2032.

__________________________

Answer 2

$\huge\bf { \red A \green N \pink S\blue W \orange E \purple R \green{...}}$

Here,

• First term, a = 52

• Common difference, d = 10

• Tn = 202

★ Formula for finding n terms of an A.P is

Tn = a + (n - 1)dTn=a+(n−1)d

= > 202 = 52 + (n - 1)10=>202=52+(n−1)10

= > 202 = 52 + 10n - 10=>202=52+10n−10

= > 202 = 42 + 10n=>202=42+10n

= > 10n = 202 - 42=>10n=202−42

= > 10n = 160=>10n=160

= > n = \frac{160}{10}=>n=

10

160

= > n = 16=>n=16

Now, we'll find sum of its n terms :-

★ Formula for finding sum of n terms of an A.P is

Sn = \frac{n}{2} (2a + (n - 1)d)Sn=

2

n

(2a+(n−1)d)

= > Sn = \frac{16}{2} (2.52 + (16 - 1)10)=>Sn=

2

16

(2.52+(16−1)10)

= > Sn = 8(104 + 150)=>Sn=8(104+150)

= > Sn = 254 \times 8=>Sn=254×8

= > Sn = 2032=>Sn=2032

hope it helps you ❣️