Question

The
8 term
an AP is 32
and 12th teen is 52.
Fund
the First term
and the Commonnce diference​

Answer 1

Answer:

d=10

a= -38

Step-by-step explanation:

i hope this is your required answer

Answer 2

GIVEN :–

• 8th term of A.P. = 32

• 12th term of A.P. = 52

TO FIND :–

• First term (a) = ?

• Common difference (d) = ?

SOLUTION :–

• We know that –

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$\bf \implies \large{ \boxed{ \bf T_n = a +(n-1)d}}$

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• According to the first condition –

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$\bf \implies T_8 = a +(8-1)d$

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$\bf \implies 32 = a +(8-1)d$

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$\bf \implies 32 = a +7d$

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$\bf \implies a +7d = 32 \: \: \: \: \: \: \: - - - eq.(1)$

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• According to the second condition –

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$\bf \implies T_12 = a +(12-1)d$

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$\bf \implies 52 = a +(12-1)d$

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$\bf \implies 52 = a +11d$

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$\bf \implies a +11d = 52 \: \: \: \: \: \: \: - - - eq.(2)$

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• Now eq.(2) - eq.(1) ,

$\bf \implies (a + 11d) - (a +7d) =52 - 32$

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$\bf \implies a + 11d- a - 7d =20$

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$\bf \implies 4d =20$

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$\bf \implies d = \cancel \dfrac{20}{4}$

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$\bf \implies \large{ \boxed{ \bf d = 5}}$

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• Now Using eq.(1) –

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$\bf \implies a +7(5) = 32$

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$\bf \implies a +35 = 32$

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$\bf \implies a = 32 - 35$

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$\bf \implies \large{ \boxed{ \bf a = - 3}}$

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• Hence , First term (a) is -3 and common difference is 5.