Question

Find the common difference of an A.P in which t18 - t14 = 32
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Answer 1

Answer:

d=8

Step-by-step explanation:

hope this will help u ......

Answer 2

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

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

$Here, \\t_{18} \\= a + (18-1)d \\= a + 17d \: --(1)\\, t_{14} \\= a + (14-1)d \\= a + 13d \: --(2)$

/* According to the problem given */

$t_{18} - t_{14} = 32$

/* From (1) and (2) */

$\implies a + 17d - ( a + 13d ) = 32$

$\implies a + 17d - a - 13d = 32$

$\implies 4d = 32$

$\implies d = \frac{32}{4}$

$\implies d = 8$

Therefore.,

$\red { Required \: common \: difference } \green { = 8 }$

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