Mathematics · Arithmetic Progressions · NCERT Examples

Example 12

A complete, independently verified solution for NCERT Example 12.

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Mathematics · Chapter 5 · NCERT Examples

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NCERT Example

sum of AP · nth term

The sum of the first 14 terms is 1050 and the first term is 10. Find the 20th term.

Board-exam working:

S_n=\frac{n}{2}[2a+(n-1)d]=\frac{n}{2}(a+l)

Given a=10,n=14,S₁₄=1050.

Use Sₙ=n/2[2a+(n−1)d].

1050=14/2[2×10+13d]=7(20+13d)=140+91d.

Thus 91d=910 and d=10.

Now a₂₀=a+19d=10+19×10=10+190=200.

200.

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