Question

Which term of the A.P. 3,10,17,... will be 84 more than its 13th term?

Answer 1

Let the first term be a = 3

Common difference , d = 7 ,

Hence the 13th term will be ,

$T_{13}$ = a + 12d

$T_{13}$ = 3 + 12×7

$T_{13}$ = 3+ 84 = 87

Since , 84 more than its 13th term ,so ,

value of term will be = 87 + 84 = 171

So value of term is 171

Now using ,

$T_n$ = a+(n-1)d

$\Rightarrow$ 171 = 3 + 7n - 7

$\Rightarrow$ 171 + 4 = 7n

$\Rightarrow$ $\frac{175}{7}$ = n

$\Rightarrow$ $T_n$ = 25 ,

So the 25th term will be 84 more than its 13th term ,

Verification :-

$T_{25}$ = a + 24 d

$T_{25}$ = 3 + 24×7

$T_{25}$ = 3 + 168

$T_{25}$ = 171