The first negative term of the A.P.62,57,52…. is thea)10th termb)14th termc)12th termd)18th termCorrect answer is option 'B'. Can you explain this answer?

Question

The first negative term of the A.P.62,57,52&#8230;. is thea)10th termb)14th termc)12th termd)18th termCorrect answer is option 'B'. Can you explain this answer?

Answer

A=62 & d=57-62= -5 tn = a+(n-1)d =a+nd-d =62+n(-5) -(-5) =62-5n+5 =67-5n .......... eq no.(1) it is a General term of this A.P For this eq (1) we take a condition is that 67-5n

Answer

Problem Analysis:
We are given an arithmetic progression (A.P.) with the first three terms as 62, 57, and 52. We need to determine the position of the first negative term in the sequence.

Solution:
To find the position of the first negative term, we need to calculate the common difference of the arithmetic progression.

Step 1: Find the common difference (d)
The common difference (d) is calculated by subtracting the second term from the first term:
d = Second Term - First Term = 57 - 62 = -5

Step 2: Find the n-th term formula
The n-th term formula for an arithmetic progression is given by:
a_n = a + (n-1)d
where a_n is the n-th term, a is the first term, n is the position of the term, and d is the common difference.

Step 3: Find the position of the first negative term
We can substitute the given values into the n-th term formula to find the position of the first negative term:
a_n = 62 + (n-1)(-5)

We want to find the value of n for which a_n is negative:
62 + (n-1)(-5) < />
-5n + 5 + 62 < />
-5n + 67 < />
-5n < />
n > 67/5
n > 13.4

Since n is the position of the term and it must be a positive integer, the first negative term occurs at the 14th position.

Therefore, the correct answer is option 'B' - 14th term.

Answer

Option (b)

Answer

Option b

Answer

Just follow the last term formula.. like lasr term will be a+(n-1)>or=0 for last positive no. 62+57....are in ap 67-(n-1)5=0 n=approx 14 this show the minimum value of n so that term will be positive..

Answer

B

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