Question

In an A.P.,if Sn = n(4n+1) ,Find the A.P.

Answer 1

sn=n(4n+1).

s1=5

5=1/2(2a)

5=1/a

5a=1

a=1/5

.....upto this crct...

after that....s2=18

18=2/2(1/5+an)

18=1/5+an

90=an+1

an=89

an =a+(n-1)d

89=1/5+88d

89*5=88d+1

445=88d+1

444=88d

88d=444

d=444/88

d=111/22

ap=a+d.... and so on ..

Answer 2

Answer:

$\huge{\pink{\boxed{\green{\sf{\therefore A.P=5,13,21.....}}}}}$

Step-by-step explanation:

$\huge{\pink{\boxed{\green{\underline{\red{\sf{SOLUTION-}}}}}}}$

$\: \: \: \: \: \: \: { \orange{ given}}\\ { \pink{ \boxed{ \green{Sn = n(4n + 1)}}}} \\ \\ { \blue{ to \: find}} \\ {\purple{ \boxed{ \red{A.P = ?}}}}$

☆ According to given question:

☆ let n be some positive integer 1,2,3,4

$\to n = 1 \\ \to Sn = n( 4n + 1) \\ \to S1 = 1(4 \times 1 + 1) \\ { \boxed{\to S1 = 5}} \\ \\ \to n = 2 \\ \to S2 = 2(4 \times 2 + 1) \\ \to S2 = 2 \times 9 \\ { \boxed{ \to S2 = 18}} \\ \\ \to n = 3 \\ \to S3 = 3(4 \times 3 + 1) \\ \to S3 = 3 \times 13 \\ { \boxed{\to s3 = 39}} \\ \\ { \boxed{ S1 =a1 = 5}} \\ \\ \to a2 = S2 - S1 \\ \to a2 = 18 - 5 \\ { \boxed{\to a2 = 13}} \\ \\ \to a3 = S3 - S2 \\ \to a3 = 39 - 18 \\ { \boxed{\to a3 = 21}} \\ \\ {\pink{ \boxed{ \green{ \therefore A.P= 5,13,21.....}}}}$

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