Question

-10) The first term is 10 and the series has a common difference of 2. How many terms are
needed to produce a sum of 252?
a) 10
b) 8
12
d) 15
c)​

Answer 1

Answer: number of terms required are 12 that is n=12

Step-by-step explanation:

We know,

Sn=$\frac{n}{2}$[2a+(n-1)d]  , where n=number of terms , a = first term , d=common difference and Sn is sum of n terms

Substituting the values we get,

252=$\frac{n}{2}$[2*10+(n-1)2]

⇒$n^{2}$+9n-252=0

⇒$n^{2}$+21n-12n-252=0             {splitting the middle term}

⇒n(n+21)-12(n+21)=0              {factorizing}

⇒(n+21)(n-12)=0

⇒n=12  , n=-21

Since 'n' is the number of terms , n cannot be negative

Hence n=12 is the correct option =)