Question

Find the sum of the first 15 terms of each of the following sequences having nth term as
(i) $a_n=3+4n$ (ii) $b_n=5+2n$ (iii) $x_n=6-n$ (iv) $y_n=9-5n$

Answer 1

Sum of 15 terms: No. of terms x (first term + last term)/2
1.

$a_n$=3+4n
$a_1$=3+4=7
l=3+4 x 15=63

Sum of 15 terms: No. of terms x (first term + last term)/2
=15(7+63)/2
=525
2.
$b_n$ =5+2n
$b_1$=7
l=35
Sum of 15 terms : No. of terms x (first term + last term)/2
=15(35+7)/2
=315
3.
$x_n$=6-n
$x_1$=6-1=5
l=6-15=-9
Sum of 15 terms : No. of terms x (first term + last term)/2
=15(5 - 9)/2
=-30
4.
$y_n$=9-5n
$y_1$=9-5=4
l=9-75=-66
Sum of 15 terms : No. of terms x (first term + last term)/2
= 15(4-66)/2
=-15 x 31
=-465