Question

If 12 +22 +32 + ... +102 = 385, then 32 +62 +92 +...+302 = ?
a) 3465
b) 3969
C) 1155​

Answer 1

Answer:

Step-by-step explanation:

1155

Answer 2

Correct Question:

If 12 +22 +32 + ... +102 = 570, then 32 +62 +92 +...+302 = ?

A) 3465

B) 3969

C) 1155​

D) 1670

Answer:

The correct option is Option D i.e. 1670.

Step-by-step explanation:

Step 1:

Given summation is a summation of an arithmetic progression (AP).

Step 2:

The AP is 32, 62, 92, ...302.

Initial term (a) = 32

Common Difference (d) = $t_n - t_{n-1}$ = 30

Number of terms (n) = $\frac{t_n - a}{d} + 1$ = $\frac{302 - 32}{30} + 1$ = 10

Last term (l) = 302

Step 3:

Sum of n terms of an AP is given by:

$S_n = \frac{n}{2} [a + l]$

$S_{10} = \frac{10}{2} [32 + 302]$

$S_{10}$ = 5 [334] = 1670

Step 4:

Hence, the correct option is Option D i.e. 1670.

#SPJ2