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Mathematics · Arithmetic Progressions · NCERT Examples

Example 16

A complete, independently verified solution for NCERT Example 16.

Mathematics · Chapter 5 · NCERT Examples

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NCERT Example

Example 16

application · sum of AP

TV production was 600 sets in year 3 and 700 in year 7, increasing uniformly. Find year 1, year 10, and total for years 1–7.

Solution

Board-exam working:

Sn=n2[2a+(n−1)d]=n2(a+l)S_n=\frac{n}{2}[2a+(n-1)d]=\frac{n}{2}(a+l)

Let first-year production be a and annual increase be d.

Then a₃=a+2d=600 and a₇=a+6d=700.

Subtracting gives 4d=100, so d=25.

Substituting in a+2d=600 gives a+50=600, hence a=550 sets.

The tenth-year production is a₁₀=a+9d=550+9×25=550+225=775 sets.

The total for the first seven years is S₇=7/2[2×550+(7−1)25]=7/2[1100+150]=7/2×1250=4375 sets.

Check: a₇=550+6×25=700, as given.

Final answer

550 sets; 775 sets; 4375 sets.