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First term of an A.P is …

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First term of an A.P is -2 and thR 10^thterm is 16. Determine the 100^thterm.

Posted by Ajay Karthikeya 8 years, 5 months ago

CBSE > Class 09 > Mathematics

2 answers

Hans Raj 8 years, 5 months ago

Given

1st term a₁ = -2 , ..............10th term a₁₀ = 16 , .................100th term a₁₀₀ = ?

we know that

an = a₁ + (n -1)d ........... a₁₀=a₁ + (10 - 1) d...................... 16 = -2 + 9d ..................... d = 18/9 ....... .... d = 2

a_{100 =}a₁ + (100 - 1) 2...........a₁₀₀ = -2 + 99x2 ........................ a₁₀₀= -2 + 198 ............... a₁₀₀= 196

0Thank You

Payal Singh 8 years, 5 months ago

First term of AP a = -2

Let common difference = d

As we know

{tex}a_n = a+(n-1)d{/tex}

=> {tex}a_{10} = a+(10-1)d{/tex}

=> 16 = -2+9d

=> 9d= 18

=> d= 2

{tex}a_{100} = a+99d{/tex}

=> {tex}a_{100}=-2+(99\times 2){/tex}

{tex}=>> a_{100}= -2+198=196{/tex}

0Thank You

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