Question

If common ratio of the G.P is 5,
5 th term is 1875, the first term is ---
(A) 3
(B) 5
(C) 15
(D) - 5​

Answer 1

Given

Common Ratio (r) = 5

T₅ = 1875

To find

First term(a)

Formula

Tₙ = arⁿ⁻¹

Now put the value on formula

T₅ = a5⁵⁻¹

1875 = a5⁴

1875 = a625

a = 1875/625

a = 3

Answer

a = 3 option (A) is correct

MORE INFORMATION ABOUT GP

Tₙ = arⁿ⁻¹

Sₙ = [a(rⁿ - 1 )]/r-1        if r>1

Sₙ = [a(1 - rⁿ)]/1 - r      if r < 1

Sₙ = na                      if r = 1

Sum of infinite GP = a/(r-1)

Answer 2

Answer:

Given :-

• The common ratio of the G.P is 5. The 5th term is 1875.

To Find :-

• What is the first term.

Formula Used :-

$\sf\boxed{\bold{\large{T_n =\: {ar}^{{n - 1}}}}}$

where,

• $\sf T_n$ = Value for the term in position n (nth term)
• a = First term
• r = The common/constant ratio
• n = Position of term

Solution :-

Given :

• Common ratio = 5
• $\sf T_5$ = 1875

According to the question by using the formula we get,

↦ $\sf T_5 =\: {(a)5}^{{(5 - 1)}}$

↦ $\sf 1875 =\: {(a)5}^{4}$

↦ $\sf 1875 =\: 625a$

↦ $\sf a =\: \dfrac{\cancel{1875}}{\cancel{625}}$

➦ $\sf\bold{\pink{a =\: 3}}$

Hence, the correct options is option no (A) 3.

$\therefore$ The first term is 3 .