Question

The sum of the series 12 22 + 32 42 + 52 62 + ... 1002 is

Answer 1

If question means 1222 instead of 12 12 then,

a=1222

d= 3242 - 1222 = 2020

an = 1002

an = a+ (n-1)d

find n

then,

Sn = n/2 (2a + (n-1) d)

Answer 2

The Sum of the given AP is 50700.

Given,

The AP series,

12, 22, 32, 42,...,1002

To find,

Sum of the given AP.

Solution,

We know that,

The general term of an AP is given by,

$a_{n}=a+(n-1)d$

Where,

$a=first term$

$d=common difference$

$n=total terms$

From the AP,

$a=12$

$d=22-12=32-22=10$

last term, $l=1002$

For $n,$

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

⇒$1002=12+(n-1)10$

⇒$1002-12=10n-10$

⇒$990+10=10n$

⇒$n=\frac{1000}{10}$

⇒$n=100$

So, there are 100 terms in the given AP.

Now, the sum of the AP,

⇒$S=\frac{n}{2}(a+l)$

⇒$S=\frac{100}{2}(12+1002)$

⇒$S=50(1014)$

⇒$S=50700$

Therefore, the sum of the given AP is, $S=50700$.