Question

first term of an ap is 10 and the difference of any it's two consecutive terms is 5 find its 48th term​

Answer 1

Answer:

48 th term = 245

Step-by-step explanation:

$first \: term \: = 10 \\ different \: between \: two \: terms = 5$

$5 \: is \: a \: prime \: its \: divide \: by \: its \: only \: \\ get \: 5$

(differencr of any two terms divide by common differents answer will be 0)

$so \: 5 \: is \: the \: common \: difference$

$48th \: term = 10 + 47 \times 5 = 245$

Answer 2

$\sf \bf \huge {\boxed {\mathbb {QUESTION}}}$

$\tt First\: term \:of\: an\: ap\: is \:10 \:and \:the\: difference\: of \:any\:its\\\tt \: two\: consecutive\: terms \:is \:5\: find\: its \:48\:th \:term.$

$\sf \bf \huge {\boxed {\mathbb {ANSWER}}}$

$\sf \bf {\boxed {\mathbb {GIVEN}}}$

• $\sf \bf a=10$
• $\sf \bf d=5$

$\sf \bf {\boxed {\mathbb {TO\:FIND}}}$

• $\sf \bf 48\:th \:term\:of\:an \:AP$

$\sf \bf {\boxed {\mathbb {SOLUTION}}}$

${\pink {\underline {\sf The\:48\:th\:term\:an\:AP}}}$

${\blue {\boxed {\boxed {\boxed {\green {\sf \bf a_n=a+\Big(n-1\Big)d}}}}}}$

• $\sf a_n=n\:th\:term\:of \:an \:AP$
• $\sf a=first\:term\:of \:an \:AP$
• $\sf d=common\:difference\:of \:an \:AP$

${\underbrace {\overbrace {\orange {\bf Substitute\:the \:values}}}}$

$\sf \bf \implies a_{48}=10+\Big(48-1\Big)5$

$\sf \bf \implies a_{48} =10+\Big(47\Big)5$

$\sf \bf \implies a_{48} =10+235$

$\implies {\blue {\boxed {\boxed {\purple {\mathfrak {a_{48} =245}}}}}}$

${\underbrace {\red {\underline {\red {\overline {\red {\sf \therefore The\:48\:th\:term\:of\:an\:AP\:is\:245}}}}}}}$

$\sf \bf \huge {\boxed {\mathbb {HOPE \:IT \:HELPS \:YOU}}}$

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$\sf \bf \huge {\boxed {\mathbb {EXTRA\:INFORMATION}}}$

$\sf \bf a_n=a+(n-1)d$

$\sf \bf S_n=\dfrac{n}{2}[2a+(n-1)d]$

$\sf \bf S_n=\dfrac{n}{2}[a+a_n]$