Question

32th term of the series 3,-2,-7,-12, ..... is​

Answer 1

S O L U T I O N :

Given,

• AP :- 3 , -2 , -7 , -12,......

To Find,

• The 32th term of an AP.

Explanation,

AP :- 3 , -2 , -7 , -12,....

=> First term (a) = 3

=> Common difference (d) = t2 - t1

=> d = -2 - 3

=> d = -5

We know that,

nth term of AP,

a_n = a + (n - 1)d

[ Put the values ]

=> a_32 = 3 + (32 - 1) × -5

=> a_32 = 3 + (31) × -5

=> a_32 = 3 - 155

=> a_32 = -152

Therefore,

The 32th term of an AP is -152.

For information,

• S_n = n/2 × (2a + (n - 1)d)
• S_n = n/2 × (a + l)

Answer 2

Given:-

• AP is 3 , -2 , -7 , - 12

To Find:-

• 32th term of the series...

Solution:-

• As we know that,

$\sf \: a = 3 \\ \\ </p><p></p><p> \sf \: d = -2 × 3 \\ \\ </p><p></p><p> \sf \: d = -5</p><p>$

• Using Formula,

${ \underline{ \boxed{ \sf{a_n = a +( n - 1) \times d}}}}$

${ \underline{ \boxed{ \sf{a_ 3\: _2 = 3 +( 32 - 1) \times - 5}}}}$

${ \underline{ \boxed{ \sf{a_ 3\: _2 = 3 +( 31) \times - 5}}}}$

${ \underline{ \boxed{ \sf{a_ 3\: _2 = 3+ ( - 155)}}}}$

${ \underline{ \boxed{ \sf{a_ 3\: _2 = - 152}}}}$

Hence Proved...