Question

First the 31st term of an AP whose 11th term is 38 and the 16th term is 73.​

Answer 1

Answer:

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Answer 2

AnswEr:

$\bold{\underline{\sf{\pink{\;\;Given\;\;}}}}$

$:\implies\sf\; a11 = a + 10d = 38$ ___eq(1)

$:\implies\sf\; a16= a + 15d = 73$ ____eq(2)

$\dag\bold{\underline{\sf{Now\; Subtracting\;(1)\; from\;(2)}}}$

$:\implies\sf\;5d = 35$

$:\implies\sf\; d = \dfrac{35}{5}$

$:\implies\large{\underline{\boxed{\sf{\red{d = 7}}}}}$

$\bold{\underline{\sf{Putting\; the\;value\;of\;d\;in\;eq(1)}}}$

$:\implies\sf\;a = 10 \times\;7 = 38$

$:\implies\sf\;a = 38 - 70$

$:\implies\large{\underline{\boxed{\sf{\red{a = - 32}}}}}$

$\rule{150}3$

$\dag\bold{\underline{\sf{We\; Know\; that}}}$

$\bigstar\large\boxed{\sf{\pink{an = a + (n -1)d}}}$

$:\implies\sf\;a + (31 - 1)d$

$:\implies\sf\; -32 + 30\times 7$

$:\implies\sf\;- 32 + 210$

$:\implies\large{\underline{\boxed{\sf{\pink{a31= 178}}}}}$

$\bold{\underline{\sf{\green{31st\; term\; of \; the\; AP\; is \; 178}}}}$

$\rule{150}3$