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.

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Answer 1

Answer:

Number of terms = 8

Explanation:

Let the number of terms of A.P. be n.

First term = a and common difference = d.

Note :-

rth term from end = (n - r + 1) th term from beginning.

2nd term from end = (n - 2 + 1) = (n - 1)th term from beginning.

T_2 = a + d = 9 - - - (i)

T_(n - 1) = a + (n - 1 -1)d = 39

T_(n - 1) = a + (n - 2)d = 39 - - (ii)

S_n = (n/2)[ 2a + (n - 1)d] = 192 - - -(iii)

Now, subtracting (i) from (ii) we get,

(n - 3)d = 30 - - -(iv)

from (i), d = (9 - a)

S_n = (n/2) [ a + a + (n - 2)d + d] = 192

=> (n/2) [ a + 39 + 9 - a ] = 192

{ from results (i) and (ii) }

(n/2) (48) = 192

n = 192 / 24 = 8

Hence, the number of terms will be 8.

Answer 2

Answer:

Explanation:

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