Question

The sum of the first m terms of ap is 4msquare -m . If its nth term is 107 , find the value of 'n' also find the 21 st term of this ap

Answer 1

Hey there !!

➡ Given :-

→ Sm  = ( 4m² - m ).

→ nth term ( An  ) = 107.

➡ To find :-

→ Value of n.

→ 21st ( a₂₁  ) term of AP.

➡ Solution :-

We have,

→ Sm  = ( 4m² - m ).

Then,

→ Sm₋₁  = 4( m - 1 )² - ( m - 1 ) .

=> Sm₋₁  = 4 ( m² + 1 - 2m ) - m + 1.

=> Sm₋₁  = 4m² + 4 - 8m - m + 1.

=> Sm₋₁  = 4m² - 9m + 5.

▶ We know that :-

→ Am  = ( Sm  - Sm₋₁  ).

=> Am  = ( 4m² - m ) - ( 4m² - 9m + 5 ).

=> Am  = 4m² - m - 4m² + 9m - 5.

=> Am  = 8m - 5.

▶ Now,

=> An  = ( 8n - 5 ).

=> 107 = 8n - 5.

=> 8n = 107 + 5.

=> n = 112/8 = 14.

▶Then,

→ a₂₁  = 8 × 21 - 5.

=> a₂₁  = 168 - 5.

=> a₂₁ = 163.

✔✔ Hence, it is solved ✅✅.

THANKS

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