Answer:

Step-by-step explanation:

a₁ = 3

a_n = 46, 875

r = 5

Find the terms between the first term and the last term.

a₂ = a₁r            a₃ = a₂r            a₄ = a₃r             a₅ = a₄r              a₆ = a₅r

a₂ = (3)(5)        a₃ = (15)(5)       a₄ = (75)(5)       a₅ = (375)(5)      a₆ = (1, 875)(5)

a₂ = 15             a₃ = 75            a₄ = 375           a₅ = 1, 875         a₆ = 9, 375

a₇ = a₆r

a₇ = (9, 375)(5)

a₇ = 46, 875

Stop with the 7th term since it is already equivalent to 46, 875. This only shows that n = 7.

Given that:

a₁ = 3

a_n = 46, 875

r = 5

n = 7

Find the sum using the formula: S_n = a₁(1 - r ⁿ)/1 - r

S₇ = 3(1 - 5⁷)/1 - 5

S₇ = 3(1 - 78, 125)/1 - 5

S₇ = 3(-78, 124)/-4

S₇ = -234, 372/-4

S₇ = 58, 593