Question

the sum of n term of an ap is 136 and common difference is 4 if the last term is 31 then find the number of terms

Answer 1

solve it by using Sn=(2a+(n-1)d)

Answer 2

Answer: The number of terms is 8.

Step-by-step explanation:

Since we have given that

Sum of n terms of an A.P. = 136

Common difference (d) = 4

Last term = 31

As we know the formula for "Last term":

$a_n=a+(n-1)d\\\\31=a+(n-1)4\\\\31=a+4n-4\\\\31+4=a+4n\\\\35=a+4n$

Similarly, we know the formula for "Sum of n terms ":

$S_n=\frac{n}{2}(2a+(n-1)d)\\\\136\times 2=n(2a+(n-1)4)\\\\372=n(2a+4n-4)\\\\\text{ using the value in eq (1)}\\\\372=n(2(35-4n)+4n-4)\\\\372=n(70-8n+4n-4)\\\\372=n(70-4n-4)\\\\372=n(66-4n)\\\\4n^2-66n+372=0\\\\2n^2-33n+136=0$

now, by using the "quadratic formula ", we get that

$n=8,n=\frac{17}{2}$

Since the value of n can't be in fraction or decimal.

Hence, the number of terms is 8.