Question

If Sn=3n^2-n
Hence, find the 20 terms.​

Answer 1

Answer:

$\huge{\pink{\boxed{\green{\sf{a20=116}}}}}$

Step-by-step explanation:

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

$\: \: \: \: \: \: {\orange{given}} \\ { \pink{ \boxed{ \green{sn = 3 {n}^{2} - n }}}} \\ \\ {\blue{to \: find}} \\ { \purple{ \boxed{ \red{a20 = }}}}$

☆ According to given question;

☆ We know sum of nth terms of an A.P

☆ So let n=1,2,3,4....

$\to n = 1 \\ \to s1 = 3 \times {1}^{2} - 1 \\ { \boxed{\to s1 = 2 }}\\ \\ \to n = 2 \\ \to s2 = 3 \times {2}^{2} - 2 \\ \to s2 = 12 - 2 \\ { \boxed{\to s2 = 10 }}\\ \\ \to n = 3 \\ \to s3 = 3 \times {3}^{2} - 3 \\ \to s3 = 27 - 3 \\ { \boxed{\to s3 = 24 }}\\ \\ \to s1 = a1 = 2 \\ \to a2 = s2 - s1 \\ \to a2 = 10 - 2 \\ { \boxed{ \to a2 = 8 }}\\ \\ \to a3 = s3 - s2 \\ \to a3 = 24 - 10 \\ { \boxed{\to a3 = 14}} \\ \\ { \boxed{\to commo \: difference = a2 - a1 = 8 - 2 = 6 }}$

☆ So we get first term and common difference :

☆ From this we can find a20:

$\to a20 = a + 19d \\ \to a20 = 2 + 19 \times 6 \\ \to a20 = 2 + 114 \\ { \pink{ \boxed{ \green{\therefore a20 = 116}}}}$

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