The question asks for the 4th term of a Geometric Progression (GP).
GP Calculation: Finding the 4th Term
We are given:
- The first term, $a = 125$.
- The common ratio, $r = \frac{2}{5}$.
The formula to find the $n^{th}$ term ($a_n$) of a GP is:
$a_n = a \cdot r^{n-1}$Step-by-Step Calculation
We need to find the 4th term, so $n=4$. Plugging the values into the formula:
- Calculate the exponent: $n-1 = 4-1 = 3$.
- Calculate $r^{n-1}$: $r^3 = \left(\frac{2}{5}\right)^3 = \frac{2^3}{5^3} = \frac{8}{125}$.
- Multiply the first term ($a$) by $r^{n-1}$: $a_4 = a \cdot r^3 = 125 \cdot \frac{8}{125}$.
- Simplify the expression: $a_4 = \frac{125 \times 8}{125} = 8$.
Therefore, the 4th term of the GP is 8.
Important Questions from Geometric Progression
In a school of 750 boys, 34% are Muslims, 42% Hindus, 12% Sikhs and the rest belong to other communities. How many boys are from other community?
Ms. Tina has 2 parents, 4 grand parents, 8 great grand parents and so on. Find the number of her ancestors during 10 (ten) generations preceeding her own.
A square is drawn by joining the midpoints of the sides of a given square. In the same way, this process continues indefinitely. If side of the first square is 4 cm, than the sum of the area of all the squares are equal to
Third term of sequence an = (-1)n(n − 7) is :
811/3 × 811/9 × 811/27 × 811/81 × ______ up to infinite term will be equal to
