Math, asked by jayeshsirvi, 3 months ago

28. In an AP, if the third term and seventh term are 4 and -8 respectively, then find which term
value is zero.​

Answers

Answered by deepakkumar9254
6

Correct Question :-

28. In an AP, if the third term and seventh term are 4 and 8 respectively, then find which term  value is zero.​

Solution :-

Third term (T_{3}) of an A.P. = 4

Seventh term (T_{7}) of an A.P. = 8

We know that -

T_{n} = a + (n-1)d

where,

a = first term of an A.P.

n = number of terms of an A.P.

d = difference of consecutive terms of an A.P.

=> T_{3} = a + (3-1)d

=> 4 = a + 2d

=> 4 - 2d = a     ....i.)

=> T_{7} = a + (7-1)d

=> 8 = a + 6d

[Substituting the value of a from eq. i.)]

=> 8 = 4 - 2d + 6d

=> 8 = 4 + 4d

=> 8 - 4 = 4d

=> 4 = 4d

=> d = 1

Finding the value of a by substituting the value of d in eq. i.)

=> a = 4 - 2d

=> a = 4 - 2 x 1

=> a = 4 - 2

=> a = 4 - 2

=> a = 2

According To the question -

T_{n} = 0 and we have to find n.

Form the formula,

=> T_{n} = a + (n-1)d

=> 0 = 2 + (n-1) x 1

=> 0 = 2 + n - 1

=> 0 = 1 + n

=> -1 = n

Here, Number of terms is -1. But n cannot be negative. So, 0 as a term does not exist in this A.P.

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