Question

the sum of 5th and 8th term of an ap is 37 and its 11th term is 32 find the AP​

Answer 1

SOLUTION :

GIVEN

• The sum of 5th and 8th term of an AP is 37

• The 11th term is 32

TO DETERMINE

The Arithmetic progression

FORMULA TO BE IMPLEMENTED

If in an arithmetic progression

First term = a and common difference = d

Then n th term of the AP is

$= \sf{a + (n - 1)d \: }$

EVALUATION

Let in the arithmetic progression

arithmetic progression First term = a and common difference = d

So

5th term = a + ( 5 - 1 ) d = a + 4d

8th term = a + ( 8 - 1 ) d = a + 7d

11th term = a + ( 11 - 1 ) d = a + 10d

So by the given condition

$\sf{ a + 4d + a + 7d = 37\: }$

$\implies \sf{ 2a + 11d = 37 \: \: \: \: \: ....(1)\: }$

Also

$\sf{ }a + 10d = 32 \: \: \: \: ....(2)$

Now 2 × Equation (2 ) - Equation (1 ) gives

$\sf{9 d = 27 }$

$\implies \sf{d = 3 }$

From Equation (2)

$\sf{a = 32 - 30 = 2}$

So

First term = a = 2

Second Term = a + d = 2 + 3 = 5

Third Term = a + 2d = 8

Fourth term = a + 3d = 11

...........

Hence the arithmetic progression is

2 , 5 , 8, 11 , .....

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LEARN MORE FROM BRAINLY

The sum of the third and seventh term

of an AP is 40 and the sum sixth and

14th terms is 70 .Find the sum of first ten terms

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