Question

The sum of first 20 terms in an arithmetic sequence is -520. If the 7th term is -5 ,find u1 and d.​

Answer 1

Answer:

answer for the given problem is given

Answer 2

$Let \: 'a' \:and \: 'd' \: are \: first \:term \: and$

$Common \: difference \: of \: an \:A.P$

$We \:know \:that ,$

$\boxed{\pink{ Sum \:of \:n\:terms (S_{n}) = \frac{n}{2}[2a+(n-1)d]}}$

$Here , n = 20$

$Sum \:of \:20 \:terms (S_{20})= -520$

$\implies \frac{20}{2}[ 2a + (20-1)d] = -520$

$\implies 10[ 2a + 19d] = -520$

$\implies 2a + 19d = \frac{-520}{10}$

$\implies 2a + 19d = - 52 \: --(1)$

$7^{th} \:term = -5 \:(given)$

$\implies a + (7-1)d = -5$

$\implies a + 6d = -5 \: --(2)$

/* Multiplying equation (2) by 2 , we get */

$\implies 2a + 12d = -10 \:--(3)$

/* Subtract equation (2) from equation (1) , we get */

$\implies 7d = -42$

$\implies d = \frac{-42}{7}$

$\implies d = -6$

/* Put d = -6 in equation (2), we get */

$a + 6(-6) = -5$

$\implies a = -5 + 36$

$\implies a = 31$

Therefore.,

$\red{ Value \: of \: a } \green { = 31}$

$\red{ and \:Value \: of \: d} \green { = -6}$

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