Question

(5 + 13 + 21 + … + 181) = ? (a) 2476 (b) 2337 (c) 2219 (d) 2139

Answer 1

QUESTION :

(5 + 13 + 21 + … + 181) = ?

(a) 2476

(b) 2337

(c) 2219

(d) 2139

ANSWER :

AP = 5 + 13 + 21 + … + 181

so this is an finite AP

now

first term=a=5

and last term=l=an= 181

also common difference=d=a2-a1

=13-5

=8

now as we know that to find the sum

no. of terms are also required

but here n=?

so,

an=l=a+(n-1)d

181=5+(n-1)8

(n-1)8=176

n-1=176/8

n=22+1

n=23

now we can use the formula to find sum of n terms

i.e Sn=(n/2) ×(a+l)

so here

Sn=?

n=23

a=5

l=181

so by putting all the required values in the formula

we get

S(23)=(23/2) ×(5+181)

S(23)=(23/2) ×(186)

S(23)=23×93

S(23)=2139

hence the required sum is 2139

hence option D is correct

IDENTITIES USED :

1. an = a+(n-1)d

2. Sn=(n/2) ×(a+l)