Home
Class 12
MATHS
In an arithmetic series, if S(n)=3n^(2)+...

In an arithmetic series, if `S_(n)=3n^(2)+2n`, find the first three terms.

Text Solution

Verified by Experts

When `n=1, S_(1)=t_(1)`. Therefore, `t_(1)=3(1)^(2)+2.1=5.`
`S_(2)=t_(1)+t_(2)=3(2)^(2)+2.2=16`
`5+t_(2)=16`
`t_(2)=11`
Therefore, d = 6, which leads to a third terms of 17. Thus, the first three terms are 5, 11, 17.
Aother common type of sequence studied at this level is a geometric sequence (or geometric progression). In a geometric sequence the ratio of any two successive terms is a constant r called the constant ration. The first n terms of a geometric sequence can be denoted by
`t_(1),t_(1)r,t_(1)r^(2),t_(1)r^(3),...,t_(1)r^(n-1)=t_(n)`
The sum of the first n terms of a geometric series is given by the formula
`Sn=(t_(1)(1-r^(n)))/(1-r)`
Promotional Banner

Topper's Solved these Questions

  • SEQUENCES AND SERIES

    ENGLISH SAT|Exercise EXERCISES|5 Videos

  • SAT MATH STRATEGIES

    ENGLISH SAT|Exercise EXAMPLE|69 Videos

  • SOLVING POLYNOMIAL INEQUALITIES

    ENGLISH SAT|Exercise EXERCISES|3 Videos

Similar Questions

Explore conceptually related problems

The nth term of a sequence is a_(n)=n^(2)+5 . Find its first three terms.

(a) The sum of 'n' terms of a progression is n(n + 1). Prove that it is an A..P. Also find its 10th term. (b) The sum of 'n' terms of a progression is (3n^(2) - 5n). Prove that it is an A.P. (c) If the sum of n terms of a series is (5n^(2) + 3n) then find its first five terms.

If the sum of n terms of a sequence is given by S_(n)=3n^(2)-2nAA n in N , then its 10th term is

The sum of n terms of an A.P. series is (n^(2) + 2n) for all values of n. Find the first 3 terms of the series:

The nth term of a series is 3^n + 2n ; find the sum of first n terms of the series.

If an = 2n, then find the first five terms of the series.