Question

find the 10th term of ap whose 4th term is 7 and 17th term is 72

Answer 1

Answer:

37 is the 10th term of the given AP

Answer 2

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

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

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

$i) 4^{th} \:term = 7 \: (given )$

$\implies a+3d = 7 \: ---(1)$

$ii) 17^{th} \: term = 72$

$\implies a+16d = 72 \: ---(2)$

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

$\implies 13d = 65$

$\implies d = \frac{65}{13}$

$\implies d = 5$

/* Put d = 5 in equation (1) , we get */

$\implies a + 3 \times 5 = 7$

$\implies a +15 = 7$

$\implies a = 7 - 15$

$\implies a = - 8$

$Now, \red{ Required \: 10^{th} \:term }$

$= a + 9d$

$= -8 + 9 \times 5$

$= - 8 + 45$

$= 37$

Therefore.,

$\red{ Required \: 10^{th} \:term }\green { = 37 }$

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