Question

in an AP, if an=2n+3, find S2

Answer 1

$\large \green{ \underline{answer}} \\ \\ \large \implies \orange{ \boxed{s2 = 12}}$

$\large \green{ \underline{question}} \\ \\ an \: = \: 2n + 3 \\ \\ \large \implies \underline \orange{to \: \: find} \\ \\ \large \implies{sum \: \: of \: \: 2nd \: \: \: terms} \\ \\ \large \implies \green{ \underline{given}} \\ \\ \large \implies {an \: = \: \: 2n + 3} \\ \\ \large \implies \green{ \underline{solution}} \\ \\ \large \implies{put \: \: n \: = 1 = 2 + 3 = 5} \\ \\ \large \implies{put \: \: n \: = 2 = 4 + 3 = 7} \\ \\ \large \implies{put \: \: n = 3 = 6 + 3 = 9} \\ \\ \large \implies{put \: \: n = 4 = 8 + 3 = 11} \\ \\ \large \implies \therefore{ \green{first \: \: term = \: a = 5}} \\ \\ \large \implies \therefore{ \green{common \: \: difference \: = d \: =7 - 5 = 2 }} \\ \\ \large \implies \underline{formula \: \: of \: \: sn} \\ \\ \large \implies \green{ \boxed{sn \: = \frac{n}{2} (2a + (n - 1)d}} \\ \\ \large \implies{s2 \: = \frac{2}{2} (2(5) + (2 - 1)2} \\ \\ \large \implies{}s2 = 1(10 + 2) \\ \\ \large \implies \green{ \boxed{s 2 =12 }}$

Answer 2

QUESTION:

in an AP, if an=2n+3, find S2

FORMULA USED :

There are two formula to find the sum;

1.

$</u><u>\</u><u>h</u><u>u</u><u>g</u><u>e</u><u>\</u><u>p</u><u>u</u><u>r</u><u>p</u><u>l</u><u>e</u><u> </u><u>{</u><u>s(n) = \frac{n}{2}</u><u>[</u><u>2a + (n - 1)d</u></p><p><u>]</u><u>}</u><u>$

where;

a = first term

d = common difference

2.

$\huge\red {s(n) = \frac{n}{2} (a + l)}$

where;

a = first term

l = last term( till where we have to find sum)

now come to main question;

Here;

an = 2n + 3

if we put n = 1 then we get the first term;

so,

$a1 = 2 \times 1 + 3 \\ a1 = 2 + 3$

$a1 = 5$

$\huge\blue {first \: term = 5}$

If we put n = 2 then we get the second term;

so,

$a2 = 2 \times 2 + 3 \\ a2 = 7$

$\huge\pink {second \: term = 7}$

now,

$\huge\green {common \: differnce = second \: term - first \: term}$

$\red {d = a2 - a1}$

so,

d = 7 - 5

d = 2

Using the formula of sum,

$s(2) = \frac{2}{2} (5 + 7) \\ s2 = 1 \times 12 \\ s(2) = 12$

$\huge\pink {sum(12) = 12}$