Question

In an AP. the first term is 25. nth term is -17 and the sum of n terms is 132. Find n and common difference

Answer 1

Answer:

Number of terms is 33

common difference is $d=\frac{-21}{16}$

Step-by-step explanation:

Formula used:

The n th term of the A.P a, a+d, a+2d, .......

is

$t_n=a+(n-1)d$

The sum of n terms of an A.P a, a+d, a+2d,.... is

$S_n=\frac{n}{2}[a+l]$

Given:

a = 25

l = -17

sum of n terms = 132

$S_n=132$

$\frac{n}{2}[a+l]=132$

$\frac{n}{2}[25+(-17)]=132$

$\frac{n}{2}[8]=132$

$4n=132$

$n=\frac{132}{4}$

$n=33$

Now,

$t_33=-17$

$a+32d=-17$

$25+32d=-17$

$32d=-42$

$d=\frac{-42}{32}$

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

Answer 2

1) t1 = a-d

=(-2)-(-2)

= -4

2) t2 = t1 - d

= (-4)-(-2)

= -6

Therefore, t1 = -4 and t2 = -6