Question

in an Ap if a5= 10 and a7 = 22 find a​

Answer 1

Answer:

$a5 = a + 4d = 10 \\ and \\ a7 = a + 6d = 22$

From the above equation

$2d = 12 \\ d = 6$

So,

$a + 4d = a + 24 = 10$

$a = - 14$

Answer 2

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

$In \:an\: Ap\: if \:{a_5} = 10\: and \:{a_7} = 22\: find \:a$

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

${a_5}=10\\ \implies {\boxed {a+4d=10}} - - (1)$

${a_7}=22\\ \implies {\boxed {a+6d=22}} - - (2)$

$Substract\: equation\: (1) \:from\: (2)$

$\cancel {+a}+6d=22\\ \cancel{ -a} -4d=-10$

____________

$\implies 2d=12$

$\implies d=\frac{12}{2}$

$\implies {\boxed {\boxed {d=6}}}$

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$Given$

$a_n=a+(n-1)d$

${a_5}=10,n=5,d=6$

$Substitute\: the\: values$

$\implies 10=a+(5-1)6$

$\implies 10=a+(4)6$

$\implies 10=a+24$

$\implies a=10-24$

$\implies{\boxed{\boxed {a=-14}}}$

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

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

$FORMULAS$

$a_n=a+(n-1)d$

$S_n=\frac{n}{2}(a+a_n)$

$S_n=\frac{n}{2}(2a+(n-1)d)$

${\mathbb{\colorbox {orange} {\boxed{\boxed{\boxed{\boxed{\boxed{\colorbox {lime} {\boxed{\boxed{\boxed{\boxed{\boxed{\colorbox {aqua} {@suraj5070}}}}}}}}}}}}}}}$