Question

In an AP the frist term is -4 and the last term is 29 and the sum of all its term is 150 find its common difference​

Answer 1

a= -4

an=29

Sn=150

an=a+(n-1)d

29= -4+(n-1)d---(1)

Sn = n/2(a+l)

150=n/2(-4+29)

150=n/2(25)

n=150/25*2

n=12

putting value of n in eqn (1)--

29= -4+(12-1)d

29= -4+11d

11d=29+4

11d=33

d=33/11

d=3

Hence, value of d=3.

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Answer 2

Given :  In an AP the first term is -4 and the last term is 29 and the sum of all its term is 150

To find : Common Difference

Solution:

First Term a  = -4

Last term l  = 29

Let say number of terms = n

Sum of n terms = (n/2)(a + l)

=> (n/2)(-4 + 29)  = 150

=> n(25) = 300

=> n = 12

l  =  a  + (n-1)d

=> 29 = -4  + (12 - 1)d

=> 33 =  11d

=> d  = 3

Common Difference = 3

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