Mark for review
What will be the sum of first 8 terms of
the given series?
1 +7 + 19 + 37 +61 +---
Answers
Sum of the series
Solution:
The given series is
1 + 7 + 19 + 37 + 61 + ...
- First term, a₁ = 1
- Second term, a₂ = 7
- Third term, a₃ = 19
- Fouth term, a₄ = 37
- Fifth term, a₅ = 61
Now, a₂ - a₁ = 7 - 1 = 6 = 1 * 6
a₃ - a₂ = 19 - 7 = 12 = 2 * 6
a₄ - a₃ = 37 - 19 = 18 = 3 * 6
a₅ - a₄ = 61 - 37 = 24 = 4 * 6
From this differences, we can find the next terms just by adding the multiple of 6 with the previous term.
• Sixth term, a₆ = a₅ + (5 * 6) = 61 + 30 = 91
• Seventh term, a₇ = a6 + (6 * 6) = 91 + 36 = 127
• Eighth term, a₈ = a₇ + (7 * 6) = 127 + 42 = 169
Now the series with 8 terms is
1 + 7 + 19 + 37 + 61 + 91 + 127 + 169
∴ the required sum is 512.
Read more on Brainly.in
1. What is the sum (-3)+(+3)+(-3)+(+3)+(-3)+(-3)+________ equal to, if the number terms is 51
- https://brainly.in/question/3530821
2. If the sum of the first n terms of an ap is 4n-n2. Find the nth term.
- https://brainly.in/question/12226728