Question

find the sum of first 25 terms of ap whose nth term is given by ax = 3x +2

Answer 1

Heya!!!

a1 = 3 ( 1 ) +2 = 5

a2 = 3 (2 ) +2 = 8

a3 = 3 ( 3 ) +2 = 11
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a25 = 3 ( 25 ) +2 = 77

5 + 8 +11 +...+ 77

It's sum is given by.

S25 = 25 / 2 [ 2 ( 5 ) + 24 × 3 ]

S25 = 1025

Answer 2

The sum of first 25 terms of ap is "1025".

Step-by-step explanation:

We have,

$a_{x} =3x+2$

To find, $S_{25}=?$

Put x = 1, 2 , ....., 25

$a_{1} =3(1)+2=5,a_{2} =3(2)+2=8,a_{3} =3(3)+2=11,$, ......

$a_{25} =3(25)+2=77$

Here, first term(a) = 5, common difference(d) = 8 - 5 = 3 and$a_{25$} = 77

The sum of first 25 terms of AP

∴ $S_{n}=\dfrac{n}{2} (a+l)$

⇒ $S_{25}=\dfrac{25}{2} (5+77)$

⇒ $S_{25}=\dfrac{25}{2} (82)=25\times 41=1025$

Hence,  the sum of first 25 terms of ap is "1025".