Question

if the sum of the first 14 term of an ap is 1050 then first term is 10 find the 20th term

Answer 1

A=10...given

S14=1050
⇒n/2[2a+(n-1)d]=1050
⇒14/2[20+13d]=1050
⇒7[20+13d]=1050
⇒20+13d=1050/7
⇒20+13d=150
⇒13d=150-20
⇒13d=130
⇒d=10

20th term=a+19d
                 =10+19×10
                 =10+190
                 =200...Answer

I hope its help you..

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Answer 2

$\huge\sf\red{Here,}$

$\large\tt\purple{S14=1050}$

$\large\tt\purple{n=14}$

$\large\tt\purple{a=10}$

$\longrightarrow$$\large\tt\pink{Sn=\frac{n}{2}(2a+(n-1)d)}$

$\longrightarrow$$\large\tt\pink{1050=\frac{14}{2}(20+13d)}$

$\longrightarrow$$\large\tt\pink{140+91d}$

$\longrightarrow$$\large\tt\pink{910=91d}$

$\longrightarrow$$\large\tt\pink{d=10}$

$\therefore$$\large\tt\green{a20=10+(2-1)×10=200,}$

$\large\tt\green{i.e,20th\:term\:is\:200}$