Question

If the 19th term of an AP is 39, find the sum of its first 37 terms​

Answer 1

$\;\;\underline{\textbf{\textsf{ Given:-}}}$

• 19th term of an AP is 39

$\;\;\underline{\textbf{\textsf{ To Find :-}}}$

• Sum of its first 37th terms

$\;\;\underline{\textbf{\textsf{ Solution :-}}}$

$\underline{\:\textsf{ We know that :}}$

$\: \boxed{\sf{ a_{n} = a + (n - 1)d}}$

$\: \boxed{\sf{ S_{n} = \frac{n}{2} 2a+ (n - 1)d}}$

$\bf\underline{\green{\:\:\:\:\:\:\:\:A.T.Q:-\:\:\:\:\:\:\:}}$

$\dashrightarrow {\sf{ a_{19} = a + (19 - 1)d }}$

$\dashrightarrow {\sf{ 39 = a + (19 - 1)d }}$

$\dashrightarrow {\sf{ 39 = a + 18d }}.......eq(1)$

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Again,

$\dashrightarrow {\sf{ s_{37} = \frac{37}{2}[ 2a + (37 - 1)d] }}$

$\dashrightarrow {\sf{ s_{37} = \frac{37}{2} [2a + 36d ]}}$

$\dashrightarrow {\sf{ s_{37} = \frac{37}{2} 2(a + 18d) }}$

$\dashrightarrow {\sf{ s_{37} = 37( a + 18d )}}$

$\dashrightarrow {\sf{ s_{37} = 37( 39 )}} \\ \\\sf From \: eq(1)$

$\dashrightarrow {\sf{ s_{37} = 1443}}$

ㅤ$\;\;\underline{\textbf{\textsf{Hence -}}}$

$\underline{\textsf{ Sum of its first 37th terms is </p><p>\textbf{1443}}}.$

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Answer 2

Step-by-step explanation:

Hey! There

1443 is the answer