Question

Ap 5,12,19 has 50 terms find its last term and find the sum of its last 15 term

Answer 1

Answer:

last term = 348

sum of last 15 terms = 4485

Step-by-step explanation:

5, 12, 19,......

a = 5 d = 7

a50 is last term

= a + 49d

= 5 + 49(7)

= 5 + 343

= 348

to find sum of last 15 terms

let us take a = 348 d = -7 n = 15

Sn = n/2 (2a + (n-1)d)

$= \frac{15}{2} (2(348) + (15 - 1) \times - 7) \\ = \frac{15}{2} (696 + 14( - 7)) \\ = \frac{15}{2} (696 - 98) \\ = \frac{15}{2} \times 598 \\ = 15 \times 299 \\ = 4485$

sum of last 15 terms is 4485

Answer 2

$\textbf{\underline{\underline{According\:to\:the\:Question}}}$

First term (a) = 5

Common difference (d) = 12 - 5 = 7

n = 50

Using formula we have

$\tt{\underline{a_{n}=a+(n-1)d}}$

$\tt{\underline{a_{n}=5+(50-1)7}}$

$\tt{\underline{a_{n}=5+49\times 7}}$

$\tt{\underline{a_{n}=5+343}}$

$\tt{\underline{a_{n}=348}}$

${\boxed{\sf\:{Sum\;of\;last\;25\;terms}}}$

First term = 348

Common Difference = - 7

n term = 15

$\tt{\rightarrow S_{n}=\dfrac{n}{2}[2a+(n-1)d]}$

$\tt{\rightarrow S_{15}=\dfrac{15}{2}[2(348)+(15-1)-7]}$

$\tt{\rightarrow S_{15}=7.5[696+(14\times -7)}$

$\tt{\rightarrow S_{15}=7.5[696-98]}$

$\tt{\rightarrow S_{15}=7.5\times 598}$

$\tt{\rightarrow S_{15}=4485}$

${\boxed{\sf\:{Sum\;of\;last\;15^th \;term=4485}}}$