Question

find numbers of term of a.p. -12,-9,-6,....,21. if 1is added to each term of the a.p. then find the sum of a.p. thus formed​

Answer 1

✪ᴀɴsᴡᴇʀ✪

• Number of terms of the AP is 12.

• Sum of terms of the new AP is 66.

★ᴇxᴘʟᴀɪɴᴀᴛɪᴏɴ★

☆ɢɪᴠᴇɴ☆

• AP:- - 12, - 9, - 6,.......,21

• 1 is added to each term to form a new AP.

☆ᴛᴏ ғɪɴᴅ☆

• Number of terms of AP.

• Sum of all terms of new AP.

᯽ғᴏʀᴍᴜʟᴀs᯽

• nth term of an AP is given by

$\:\:\:\:\:\:\: a_n = [ a + (n - 1)d]$

• Sum upto nth term is given by

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

$\:\:\:\:\:\:\: S_n = \frac{n}{2}[a + l]$

where $l$ is the last term of the AP.

☆ᴄᴀʟᴄᴜʟᴀᴛɪᴏɴ☆

Number of Terms

The given AP is - 12, - 9, - 6,.......,21.

Here,

• $a = - 12$
• $d = - 9-(-12) = 3$
• $a_n = 21$

Using these in the first formula, we get

$\to 21 = [ - 12 + (n - 1)\times(3)]$

$\to 21 = [ - 12 + 3n - 3 ]$

$\to 21 = - 15 + 3n$

$\to 21 + 15 = 3n$

$\to 36 = 3n$

$\to n = 12$

Hence, number of terms of the AP is 12.

Sum of AP

Adding 1 to each terms of the original AP, the new AP formed is

- 11, - 8, - 5,....... 22.

Here

• $a = - 11$
• $d = - 8 - (-11) = 3$
• $n = 12$

Using these in the second formula, we get

$\to S_n = \frac{n}{2}[a + l]$

$\to S_n = \frac{12}{2}[-11 + 22]$

$\to S_n = 6\times 11$

$\to S_n = 66$

Hence, sum of terms of the new AP is 66.

Answer 2

Answer:

The correct answer is 66

Step-by-step explanation:

using the formula :

$an = a + (n - 1)d$

we will get n = 12.

The using the formula

$sn = \frac{n}{2} (a + l)$

we can take n = 12, a = -11 and d = 22

by doing all calculations we will get final answer 66.

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