Question

An arithmetic progression 5,12,19........ has 50 term find its last terms . Hence find the sum of its last 15 term

Answer 1

a=5 d= 7 n = 50
an = a+(n-1)d
an = 5+49*7
an = 5+343 = 348
15th term of ap is
a15 = 5+ 14*7= 5+98=103

Answer 2

a50 = 5 + 49 × 7  

= 5 + 343 = 348  

a36 = 5 + 35 × 7 = 250

Required sum = $\bf\huge\frac{15}{2} [250+348]$

$\bf\huge\frac{15}{2} [598]$

= 4485