Question

Here's a question for all MathsAryaBhatt :-

Please solve this question ⬆⬆​

Answer 1

Answer :

First term = 8

Total terms = 59

Step by step explanation :

Given :

The 2nd, 31st and last term of an AP is 31/4 , 1/2 and -13/2.

To find » First term and number of terms.

Solution :

Given that, 2nd term is 31/4, we can say that :

a + d = 31/4

» 4a + 4d = 31..(1)

Also, 31st term » 1/2

» a + 30d = 1/2

» 2a + 60d = 1..(2)

Multiplying the eq.(2) by 2 on both sides,

.°. 2(2a + 60d) = 2 × (1)

» 4a + 120d = 2..(3)

From eq. (3) and eq.(1) ,

4a + 4d = 31

- 4a + 120d = 2

________________

» -116d = 29

» d = -1/4

Therefore,

4a + 4( -1/4 ) = 31

» 4a = 32

» a = 8

Hence, we get the first term as 4.

Now,

First term = 8

Last term = -13/2

Using the formula,

a + (n - 1)d = -13/2

» 8 + (n - 1) × -1/4 = -13/2

» 8 - (n/4) + (1/4) = -13/2

» n/4 = 8 + 1/4 + 13/2

» n/4 = (32 + 1 + 26) / 4

» n = 59

Thus, there are total 59 terms in the AP.

Answer 2

Answer lies in the attachment.