Question

find the sum of first 50 terms of an A.P whose nth term is ( 3n + 7 )​ . please explain . ​

Answer 1

${S{ \tiny{50}} = 4175}$

Step-by-step explanation:

Given -

• nth term of an A.P is 3n + 7.

To find -

• Sum of first 50 terms of the A.P .

Solution -

$a{ \tiny{n}} = 3n + 7$

$\longmapsto \: a{ \tiny{1}} = 3(1)+ 7$

$\longmapsto \: a{ \tiny{1}} = 10$

$\longmapsto \: a{ \tiny{2}} = 3(2)+ 7$

$\longmapsto \: a{ \tiny{2}} = 6 + 7$

$\longmapsto \: a{ \tiny{2}} = 13$

$\longmapsto \: a{ \tiny{3}} = 3(3) + 7$

$\longmapsto \: a{ \tiny{3}} = 9+ 7$

$\longmapsto \: a{ \tiny{3}} = 16$

Similarly we can continue to find the successive terms of the A.P .

$d = a{ \tiny{2}} - a{ \tiny{1}}$

$\longmapsto d = 13 - 10$

$\longmapsto \blue{d = 3}$

Now , formula for sum of 'n' terms of an A.P is,

$\large{S{ \tiny{n}}= \Large{\frac{n}{2}} [2a+(n−1)d]}$

On putting the values in the equation , we get ,

$\longmapsto \: S{ \tiny{50}}= \large{\frac{ \cancel{50}}{ \cancel2}} [2(10)+(50−1)3]$

$\longmapsto \: \large{S{ \tiny{50}}= 25 [20+(49) 3]}$

$\longmapsto \: \large{S{ \tiny{50}}= 25 [20+147]}$

$\longmapsto \: \large{S{ \tiny{50}}= 25 [167]}$

$\longmapsto \: \orange{ \boxed {S{ \tiny{50}} = 4175}}$

Answer 2

Step-by-step explanation:

Sn = 4175

$\: \: \:$