Question

Use the formula for the sum of the first n terms of a geometric sequence to solve. Find the sum of the first four terms of the geometric sequence: 2, 10, 50, . . . .

a) 19
b) 312
c) 62
d) 156

Answer 1

The 1st 4 numbers in this sequence will be 2,10,50,250 as the common multiplier=5

So sum of all 4 numbers will be=2+10+50+250=312 (Answer)

Answer 2

Answer:  The correct option is (b) 312.

Step-by-step explanation:  We are given to use formula to find the sum of first four terms of the following geometric sequence :

2,  10,  50,   .   .   .  

We know that

the sum of first n terms of a geometric sequence with first term a and common ratio r is given by

$S_n=\dfrac{a(r^n-1)}{r-1}.$

For the given geometric sequence, we have

first term, a = 2

and the common ratio, r is given by

$r=\dfrac{10}{2}=\dfrac{50}{10}=~~.~~.~~.~~=5.$

Therefore, the sum of first four terms of the given geometric sequence is

$S_4=\dfrac{a(r^4-1)}{r-1}=\dfrac{2(5^4-1)}{5-1}=\dfrac{2\times 625-1}{4}=\dfrac{624}{2}=312.$

Thus, the required sum of first four terms is 312.

Option (b) is CORRECT.