Question

find 31 term of ap were 11term is 38 and 16 term is 73​

Answer 1

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find 31 term of ap were 11term is 38 and 16 term is 73

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Given :11th term (a+10d)=38

$= > a = 38 - 10d....(1)$

16th term is 73

$a16 = a + 15d = 73$

Put a's value from equation 1

$= > a + 15d$

$= 38 - 10d + 15d = 73$

$= 38 + 5d = 73$

$= > 5d = 73 - 38$

$= > 5d = 35$

$\bold{\boxed{\blue{d = 7}}}$

Put D's value in equation 1

$a = 38 - 10d$

$= > a = 38 - 10 \times 7 = 38 - 70$

$\bold{\boxed{\red{ a = - 32}}}$

Now ,finding 31st term

$a31 = a + 30d$

$= {\red{- 32 }}+ 30 \times {\blue{7 }}= - 32 + 210$

$= 178$

Hence ,31st term is 178.

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