Question

The second term from beginning and end of an A.P. are 9 and 39 respectively. If the sum of its terms is 192, then the number of terms will be. plz answer me fast​

Answer 1

Answer:

yeh lo mai aa gya kon hu mai ????

Answer 2

The total number of terms in this AP is 8.

GIVEN: The second term from the beginning and end of an A.P. are 9 and 39 respectively. The Sum of all the terms is 192.
TO FIND: The total number of terms (n)
SOLUTION:

As we are given,

The second term of the AP from the beginning = 9

The Second term of the AP from the end = 39

Also

Sum of all the terms = 192

Now,

Let us assume that:

The first term of AP is 'a'

The Common difference is 'd'

The total number of terms is 'n'

As we know,

a₂ = a + (2 - 1)d = 9                                                   (We are given this)

a + d = 9

Also,

aₙ₊₁ = a + (n - 2)d = 39                                               (We are given this)

As we also know,

Sum of all its terms is 192

Therefore,

Sum of n terms  = n/2 [a + aₙ]

n/2 [a + aₙ]  = 192

n[a + (39 + d)] = 384

n[a + d + 39] = 384

n[39 + 9] = 384

48n = 384

n = 8

Therefore,

There are 8 terms in the AP.

SPJ2