Question

If 11th term of AP is 38 and 16th term is 73 then its first term is

Answer 1

$Let \: a \:and \:d \:are \: first \:term \:and \\common \: difference \: of \:an \:A.P$

$\boxed { \pink { n^{th} \:term \:of \:A.P (a_{n}) = a+(n-1)d }}$

$11^{th}\:term = 38\:(given)$

$\implies a + (11-1)d = 38$

$\implies a + 10d = 38\: ---(1)$

$16^{th}\:term = 73 \:(given)$

$\implies a + (16-1)d = 73$

$\implies a + 15d = 73 \: ---(2)$

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

$\implies 5d = 35$

$\implies d = \frac{35}{5}$

$\implies d = 7$

/* Put d = 7 in equation (1) ,we get */

$\implies a + 10 \times 7 = 38$

$\implies a + 70 = 38$

$\implies a = 38 - 70$

$\implies a = -32$

Therefore.,

$\red { First \:term \:of \: given \:A.P }\green {= -32}$

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