Question

37. The sum of the AP 2,7,12,....to 10 terms
A) 180
B) 110
C) -180
D) -170​

Answer 1

$\huge{\mathtt{\pink{꧁ AnSwEr ꧂}}}$

Answer

the sum of the 10 terms of the

given AP is 245.

Complete step by step solution:

We are given that the A.P.2, 7, 12,....

We know that the arithmetic progression is a sequence of numbers in order in which the difference of any two consecutive numbers is a constant value. We will now find the first term a and the

second term b of the given

a = 2

second term=7

Subtracting the second term from the first

term to find the common difference of the given A.P., we get

⇒d 7-2 ⇒d=5

We will use the formula of sum of n terms of the arithmetic progression A.P., that is, Sn = (2a + (n − 1) d), where a is the first term and d is the common difference,

We know that n = 10.

Substituting these values of n, a in the above formula for the sum of the

arithmetic progression, we get

10

⇒ S10 = (2 (2) + (10-1) 5)

2

→S10=5(4+9 (5))

S10 = 5(4+45) ⇒ S10 = 5 (49)

→ S10 = 245

Thus, the sum of the 10 terms of the

given AP is 245.

Hope it helps

pls mark me brainliest

Answer 2

Step-by-step explanation:

$\huge \color{red} \boxed{ \mathfrak{ \colorbox{cyan}{Given :-}}}$

$\implies \mathtt{first \: term,a = 2}$

$\implies \mathtt{common \: difference,d_1= a_2-a_1 = 7 - 2 = 5}$

$\implies \mathtt{number \: of \: terms ,n= 10}$

$\mathtt{ \implies \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: d_2= a_3-a_2 = 12 - 7 = 5}$

$\huge \color{orange} \boxed{ \mathfrak{ \colorbox{cyan}{To find :-}}}$

$\mathtt{sum \: of \: 10 \: terms}$

$\mathtt{We \: know \: that,}$

$S_n = \frac{n}{2} (2a + (n - 1)d)$

$S_{10} = \frac{10}{2} (2(2)+ (10- 1)5)$

$S_{10} = \frac{10}{2} (4+ 45)$

$S_{10} = 5 (49)$

$\boxed{ S_{10} = 245}$

$\color{brown} \mathfrak{Hence \: the \: sum \: of \: 10 \: terms \: are \: 245}$