Examkin

Question

Difficulty: MediumArithmetic and Geometric Progressions (AP and GP)

The sum of the first nn terms of an arithmetic progression (A.P.) is 210210. If the first term is 33 and the last term is 3939, what is the value of nn?

  1. 10Answer
  2. B
    11
  3. C
    5
  4. D
    9

Answer

The number of terms nn is 1010.
Using the standard sum formula Sn=n2(a+l)S_n = \frac{n}{2}(a + l) for an A.P. with known first term a=3a = 3 and last term l=39l = 39, we set 210=n2(3+39)=21n210 = \frac{n}{2}(3 + 39) = 21n. Solving for nn gives n=10n = 10.

Step-by-Step Solution

1
Identify the given parameters of the arithmetic progression.
First term a=3a = 3, last term l=39l = 39, and sum Sn=210S_n = 210.
These values are required to apply the sum formula for an A.P.
2
Apply the sum formula Sn=n2(a+l)S_n = \frac{n}{2}(a + l).
210=n2(3+39)=n2(42)=21n210 = \frac{n}{2}(3 + 39) = \frac{n}{2}(42) = 21n.
The sum of nn terms in an A.P. with a known first and last term is given by n2(a+l)\frac{n}{2}(a + l).
3
Solve for nn.
n=21021=10n = \frac{210}{21} = 10.
Dividing the total sum by 2121 gives the exact number of terms.

Key Concept

Sum of an Arithmetic Progression using first and last terms
Estimated Time:1m 30s
Rate this question

Topics

Arithmetic and Geometric Progressions (AP and GP)

More questions from this topic