Question

I an a. P a is 25,tn is -17 ,Sn is 132 find the d and n

Answer 1

In the Arithmetic Sequence
first term i.e. a = 25
nth term i.e. tn = -17
this is a decreasing Arithmetic Sequence
Summation of terms Sn = 132
now,
tn = a+ (n-1)d
where n is no. of terms and d is common difference between two consecutive terms.

$- 17 = 25 + (n - 1) \times d$
this is equation no. 1

Sn = n( a + tn )/2
$132 = n \times (25 - 17) \div 2$
this is equation no. 2

Now, finding the value of n from 2nd equation and and putting it in first will give you the value of d.

$n = 33$
$d = \frac{ - 21}{16}$