Question

The sum of 15 th and 20 th terms of an AP is 80. Its 28th term is 60 , Find 7th term.

Answer 1

$\sf\huge\underline\blue{Given:-}$

• Sum of 15th and 20th terms=80
• 29th terms of AP=60

$\sf\huge\underline\blue{To\:Find:-}$

• 7th terms of AP=?

$\sf\huge\underline\blue{Solution:-}$

• Formula using here 1st

$\rm{\longrightarrow a+(n-1)d}$

$\rm{\longrightarrow a+14d+a+19d=80}$

$\rm{\longrightarrow 2a+33d=80-----(1)}$

• Second equation here

$\rm{\longrightarrow a+27d=60-----(2)}$

• we will multiply by 2 in equation 2

$\rm{\longrightarrow 2a+33d=80}$

$\rm{\longrightarrow 2a+54d=120}$

• if we solve here than we get d=?

$\rm{\longrightarrow 21d=40=d=40/21}$

• putting value of d=40/21 in 2

$\rm{\longrightarrow a+27(40/21)=60}$

$\rm{\longrightarrow a+360/7=60}$

$\rm{\longrightarrow a=60-360/7}$

$\rm{\longrightarrow a=420-360/7}$

$\rm{\longrightarrow a=60/7}$

• Calculate 7th term

$\rm{\longrightarrow a+(n-1)d}$

$\rm{\longrightarrow 60/7+6(40/21)}$

$\rm{\longrightarrow 60/7+80/7}$

$\rm{\longrightarrow 60+80/7}$

$\rm{\longrightarrow 140/7=20}$