Question

The first and the last terms of an AP are 10 and 361 respectively. If its common difference is 9 then find the number of terms and their total sum?

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Answer 1

Given

• First term, a = 10
• Last term, al = 361
• Common difference, d = 9

As we know that

al =a + (n −1)

⟹ 361 = 10 + (n − 1)9

⟹ 361 = 10 + 9n − 9

⟹ 361 = 9n + 1

⟹ 9n = 360

⟹ n = 40

Therefore, total number of terms in AP = 40

Now, sum of total number of terms of an AP is given as:

Sn = n/2 [2a + (n − 1)d]

⟹ S40 = 40/2 [2 × 10 + (40 − 1)9]

= 20|20 + 39 x 9]

=20[20 + 351]

=20 × 371 = 7420

Thus, sum of all 40 terms of AP = 7420.

Answer 2

Answer:

n = 40,  S40 = 7420

Step-by-step explanation:

a = 10      d = 9

l ( an) = 361

n = ?

l = a + (n-1) d

361 = 10 + (n-1) 9

351 = (n-1) 9

351/9 = n-1

39 = n-1

n = 40

Sn = n/2 ( a + l )

S40 = 40/2 ( 10 + 361 )

S40 = 20 ( 371 )

Therefore, S40 = 7420

Thank You =)