Here's a question for all MathsAryaBhatt :-
Please solve this question ⬆⬆

Answers
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 lies in the attachment.

