Question

What is the sum of the first 10 terms for 1 + 4 + 16 +64 + ...?

Answer 1

349525

Explanation:

Sum of a Geometric Sequence

• Sₙ = a(rⁿ - 1) / (r - 1)

Taking :

• a = 1
• r = 4
• n = 10

Solving

• S₁₀ = 1(4¹⁰ - 1) / 4 - 1
• S₁₀ = 1048576 - 1 / 3
• S₁₀ = 1048575/3
• S₁₀ = 349525

Answer 2

`\huge\color{pink}\boxed{\colorbox{Black}{♔︎Answer♔︎}}`

349525

Explanation:

`= \textsf{\underline{\large{To find :-}}}`

The sum of first 10 terms

`\textsf{\underline{\large{Given :-}}}`

a = 1

r = 4

`\sf{ \huge{ \underline{ \underline {Solution :-}}}}`

`\sf S_n = \frac{a( {r}^(n) - 1)}{(r - 1)} ,if \: r ≠ 1`

here n = 10

we just need to substitute the value

`\sf \implies S_(10) = \frac{1( {4}^(10) - 1) }{(4 - 1)} \\ \\ \sf \implies S_(10) = \frac{ {4}^(10) - 1 }{3} \\ \\ \sf \implies S_(10) = (1048576 - 1)/(3) \\ \\ \sf \implies S_(10) = (1048575)/(3) \\ \\ \sf { \red{ \implies S_(10) = 349525}}`