Question

In an A.P. 17th term is 7 more than its 10th term. Find the common difference.
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Answer 1

${\underline{\underline{\frak{Given\::}}}}$

• 17th term of an AP is 7 more than 10th term.

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${\underline{\underline{\frak{To\:Find\::}}}}$

• Common difference?

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${\underline{\underline{\frak{Solution\::}}}}$

$\underline{\bigstar\:\boldsymbol{According\:to\:the\: Question\::}}$

$:\implies\sf a_{17} = a_{10} + 7$

$:\implies\sf a + 16d = a + 9d + 7$

$:\implies\sf 16d = 9d + 7$

$:\implies\sf 16d - 9d = 7$

$:\implies\sf 7d = 7$

$:\implies\sf d = \cancel{ \dfrac{7}{7}}$

$:\implies{\boxed{\sf{\purple{d = 1}}}}\;\bigstar$

$\therefore\;{\underline{\sf{Hence,\;Common\; difference\;of\;an\;AP\:is\; \bf{1}.}}}$

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$\qquad\qquad\boxed{\underline{\underline{\bigstar \: \bf\:Formula\:Related\:to\:AP\:\bigstar}}}$

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$\sf (i)\;The\; n^{th}\;term\;of\;an\;AP\; = \; \red{a_n + (n - 1)d}$

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$\sf (ii)\;Sum\;of\;n\;term\;of\;an\;AP\; = \; \purple{S_n = \dfrac{n}{2} \bigg\lgroup\sf 2a + (n - 1)d \bigg\rgroup}$

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$\sf (iii)\;Sum\;of\;all\;terms\;of\;AP\;having\;last\:term\;as\;'l'\; = \; \pink{ \dfrac{n}{2}(a + l)}$