Question

obtain the sum of first 48th term of an A.P whose 21st term is 72 &28 term is 156​

Answer 1

Answer:

5432

Step-by-step explanation:

see from the above pic u will find ur answer

Answer 2

Answer:

Given:

• $a_{21} = 72$
• $a_{28} = 156$

To find:

• $S_{48}$ in the AP

$\sf{\underline{Solution:-}}$

First we will solve the equations , then we will have the first term and common difference in the AP

☘Used formula:

$\boxed{a_n = a+ (n-1)d}$

✦Taking first equation:

➫$a_{21} = 72$

➫$a + (21 - 1)d = 72$

➫$a + 20d = 72$ -(i)

✦Taking second equation:

➫$a_{28} = 156$

➫$a + (28 - 1)d = 156$

➫$a + 27d = 156$ -(ii)

➣Subtracting (i) and (ii):

➫$a+ 20d - a - 27d = 72 - 156$

➫$-7d = -84$

➫$d = 12$

$\implies a = -168$

Now finding sum to 48 terma

☘Used formula:

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

✦Putting all the values:

➫$S_{48} = \dfrac{48}{2} [2(-168) + (48 - 1)12]$

➫$S_{48} = 24[- 336 + 564]$

➫$S_{48} = 24 \times 228$

➫$S_{48} = 5472$

•°•Hence the sum to 48 terms is 5472