Question

the sum of 'n' terms of two AP are in the ratio 5n - 3 : 4n + 18. ratio of their 11th term is?

Answer 1

Answer:

terms

Step-by-step explanation:

terms of two ap are their 11th term is.

Answer 2

Let one AP be of the form

$a_{1}$ + $a_{2}$ +......+$a_{n}$ = $S_{a}$

Let other AP be of the form

$b_{1}$ + $b_{2}$ +.....+$b_{n}$ = $S_{b}$

$S_{a}$ : $S_{b}$ = 5n-3 : 4n+18

For various terms in AP we know that 11th term is mean of first and 21st term of AP

So $a_{11}$ = $\frac{a_{1} + a_{21} }{2}$

$b_{11} = \frac{b_{1} + b_{21} }{2}$

$a_{11}$ : $b_{11}$ = $\frac{a_{1} + a_{21} }{b_{1} + b_{21}}$

= $\frac{S_{a for 21 terms} }{S_{b for 21 terms} }$

Note:- (How? As sum = $\frac{firstterm + lastterm}{2}$(number of terms) )

= $\frac{5(21) - 3}{4(21) + 18}$

= $\frac{102}{102}$

=1