Question

the sum of 5th and 7th terms of an A. P is 56 and the 13th term is 42. find the A. P.​

Answer 1

Answer:

Given -

The sum of 5th and 7th terms of an A. P is 56 and 13th term is 42

To Find -

The A. P

Solution -

∴a+4d+a+6d=52

⇒2a+10d=52⟶(1)

And, the 10th term is 46.

∴a+9d=46

multiplying it by 2 we get,

2a+18d=92⟶(2)

Solving equations (1) and (2) we get,

8d=40

⇒d=5

Substituting the value of d in (1) we get,

2a+(10×5)=52

⇒2a=52−50

⇒a=1

Therefore, the required A.P. is,

1,6,11,16,21,26,31,.....

Thank You

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Answer 2

Answer:

∴Given, sum of the 5th and 7th term is 56.

∴a+4d+a+6d=56

⇒2a+10d=56⟶(1)

And, the 10th term is 42.

∴a+9d=42

multiplying it by 2 we get,

2a+18d=92⟶(2)

Solving equations (1) and (2) we get,

8d=40

⇒d=5

Substituting the value of d in (1) we get,

2a+(10×5)=56

⇒2a=52−50

⇒a=1

Therefore, the required A.P. is,

1,6,11,16,21,26,31,.....