You visited us 1 times! Enjoying our articles? Unlock Full Access!

Sum of N Terms of an AP

Consider a se...

Question

Consider a sequence whose sum to $n$ terms is given by the quadratic function $S_{n} = 3 n^{2} + 5 n$ then sum of the squares of the first three terms of the given series is,

1100

No worries! We‘ve got your back. Try BYJU‘S free classes today!

660

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

799

No worries! We‘ve got your back. Try BYJU‘S free classes today!

1000

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is B $660$
Given: $S_{n} = 3 n^{2} + 5 n$

$T_{n} = S_{n} - S_{n - 1}$

$T_{n} = (3 n^{2} + 5 n) - (3 {(n - 1)}^{2} + 5 (n - 1))$

$T_{n} = (3 n^{2} + 5 n) - (3 (n^{2} - 2 n + 1)) - 5 n + 5$

$T_{n} = 3 n^{2} + 5 n - 3 n^{2} + 6 n - 3 - 5 n + 5$

$T_{n} = 6 n + 2$

Again $T_{1} = 6 \times 1 + 2 = 8, T_{1}^{2} = 8^{2} = 64$

$T_{2} = 6 \times 2 + 2 = 14, T_{2}^{2} = 14^{2} = 196$

$T_{3} = 6 \times 3 + 2 = 20, T_{3}^{2} = 20^{2} = 400$

$∴ T_{1}^{2} + T_{2}^{2} + T_{3}^{2} = 64 + 196 + 400 = 660$

Hence option $B$ is the answer

Suggest Corrections

Similar questions

n

S_{n} = 3 n^{2} + 5 n

n

S_{n} = 3 n^{2} - 5 n + 7

t_{r}

r^{t h}

n

S_{n} = 3 n^{2} - 5 n + 7

t_{r}

r^{t h}

n

S_{n} = 3 n^{2} + 3 n

6^{t h}

S n = 3 n^{2} + 5 n

Join BYJU'S Learning Program